6.2: The Role of Management
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1. What is the role of management?
Management is the process of guiding the development, maintenance, and allocation of resources to attain organizational goals. Managers are the people in the organization responsible for developing and carrying out this management process. Management is dynamic by nature and evolves to meet needs and constraints in the organization’s internal and external environments. In a global marketplace where the rate of change is rapidly increasing, flexibility and adaptability are crucial to the managerial process. This process is based in four key functional areas of the organization: planning, organizing, leading, and controlling. Although these activities are discussed separately in the chapter, they actually form a tightly integrated cycle of thoughts and actions.
From this perspective, the managerial process can be described as (1) anticipating potential problems or opportunities and designing plans to deal with them, (2) coordinating and allocating the resources needed to implement plans, (3) guiding personnel through the implementation process, and (4) reviewing results and making any necessary changes. This last stage provides information to be used in ongoing planning efforts, and thus the cycle starts over again. The four functions are highly interdependent, with managers often performing more than one of them at a time and each of them many times over the course of a normal workday.
Exhibit 6.2 To encourage greater collaboration between employees, Apple is investing $5 billion in the construction of its new Cupertino, CA, headquarters, which is replacing several buildings the company had outgrown. Most headquarters-based employees of Apple now share not only the same office space, but also the same technology tools and corporate culture. How do Apple’s planning and organizing decisions increase organizational efficiency and effectiveness? (Credit: Tom Pavel / flickr/ Attribution 2.0 Generic (CC BY 2.0))
The four management functions can help managers increase organizational efficiency and effectiveness. Efficiency is using the least possible amount of resources to get work done, whereas effectiveness is the ability to produce a desired result. Managers need to be both efficient and effective in order to achieve organizational goals. For example in 2016, Delta, one of the most efficient network U.S. airlines, operated at revenue of 12.15 cents per seat-mile, which is the revenue the company makes on one seat (occupied or not) the distance of one mile. No other airline came close to operating this efficiently except Southwest, which flew seats that produced 12.51 cents a mile, the best performance of all U.S. airlines. 1 There are many ways that airlines can manage to produce higher revenue per seat-mile. For instance, they can raise ticket prices, fill more of their seats, operate more efficient aircraft that utilize less fuel, or negotiate favorable salaries with their employees. While efficiency and effectiveness are sometimes lauded by investors, airlines also need to account for customer satisfaction, which can mean extra costs. 2
To meet the demands of rapid growth, Skechers hired a new chief financial officer, John Vandemore, which allowed their existing CFO (David Weinberg) to concentrate on international expansion. Skechers CEO Robert Greenberg commented: “As international now represents more than 50 percent of our total business, we must continue to ramp up operations and infrastructure to meet the demand. David (Weinberg) understands how to do it the right way at the right speed to maintain our forward momentum. With John (Vandemore) handling CFO responsibilities, David will now have the bandwidth to travel and find opportunities to maximize our efficiencies around the globe.” 3
As these examples and Table 6.1 show, good management uses the four management functions to increase a company’s efficiency and effectiveness, which leads to the accomplishment of organizational goals and objectives. Let’s look more closely at what each of the management functions entails.
| What Managers Do and Why | |||||
|---|---|---|---|---|---|
| Good management consists of these four activities: | Which results in | And leads to | |||
Planning
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Leading
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||||
Organizing
|
Controlling
|
Leads to | Organizational efficiency and effectiveness | Leads to | Achievement of organizational mission and objectives |
Table 6.1
CONCEPT CHECK
- Define the term management .
- What are the four key functions of managers?
- What is the difference between efficiency and effectiveness?


43.1: Mean
Lesson
Let's explore the mean of a data set and what it tells us.
Exercise \(\PageIndex{1}\): Close to Four
Use the digits 0–9 to write an expression with a value as close as possible to 4. Each digit can be used only one time in the expression.
Exercise \(\PageIndex{2}\): Spread Out and Share
- The kittens in a room at an animal shelter are arranged in five crates, as shown.
- The manager of the shelter wants the kittens distributed equally among the crates. How might that be done? How many kittens will end up in each crate?
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The number of kittens in each crate after they are equally distributed is called the
mean
number of kittens per crate, or the
average
number of kittens per crate.
Explain how the expression \(10\div 5\) is related to the average. -
Another room in the shelter has 6 crates. No two crates contain the same number of kittens, and there is an average of 3 kittens per crate.
Draw or describe at least two different arrangements of kittens that match this description. You may choose to use the applet to help.
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Five servers were scheduled to work the number of hours shown. They decided to share the workload, so each one would work equal hours.
Server A: 3
Server B: 6
Server C: 11
Server D: 7
Server E: 4
- On the grid on the left, draw 5 bars whose heights represent the hours worked by servers A, B, C, D, and E.
- Think about how you would rearrange the hours so that each server gets a fair share. Then, on the grid on the right, draw a new graph to represent the rearranged hours. Be prepared to explain your reasoning.
- Based on your second drawing, what is the average or mean number of hours that the servers will work?
- Explain why we can also find the mean by finding the value of \(31\div 5\).
- Which server will see the biggest change to work hours? Which server will see the least change?
Are you ready for more?
Server F, working 7 hours, offers to join the group of five servers, sharing their workload. If server F joins, will the mean number of hours worked increase or decrease? Explain how you know.
Exercise \(\PageIndex{3}\): Getting to School
For the past 12 school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown in the table.
\(9\qquad 8\qquad 6\qquad 9\qquad 10\qquad 7\qquad 6\qquad 12\qquad 9\qquad 8\qquad 10\qquad 8\)
- Find the mean for Mai’s data. Show your reasoning.
- In this situation, what does the mean tell us about Mai’s trip to school?
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For 5 days, Tyler has recorded how long his walks to school take in minutes. The mean for his data is 11 minutes. Without calculating, predict if each of the data sets shown could be Tyler’s. Explain your reasoning.
- data set A: 11, 8, 7, 9, 8
- data set B: 12, 7, 13, 9, 14
- data set C: 11, 20, 6, 9, 10
- data set D: 8, 10, 9, 11, 11
- Determine which data set is Tyler’s. Explain how you know.
Summary
Sometimes a general description of a distribution does not give enough information, and a more precise way to talk about center or spread would be more useful. The mean , or average , is a number we can use to summarize a distribution.
We can think about the mean in terms of “fair share” or “leveling out.” That is, a mean can be thought of as a number that each member of a group would have if all the data values were combined and distributed equally among the members.
For example, suppose there are 5 bottles which have the following amounts of water: 1 liter, 4 liters, 2 liters, 3 liters, and 0 liters.
To find the mean, first we add up all of the values. We can think of as putting all of the water together: \(1+4+2+3+0=10\).
To find the “fair share,” we divide the 10 liters equally into the 5 containers: \(10\div 5=2\).
Suppose the quiz scores of a student are 70, 90, 86, and 94. We can find the mean (or average) score by finding the sum of the scores \((70+90+86+94=340)\) and dividing the sum by four \((340\div 4=85)\). We can then say that the student scored, on average, 85 points on the quizzes.
In general, to find the mean of a data set with \(n\) values, we add all of the values and divide the sum by \(n\).
Glossary Entries
Definition: Average
The average is another name for the mean of a data set.
For the data set 3, 5, 6, 8, 11, 12, the average is 7.5.
\(3+5+6+8+11+12=45\)
\(45\div 6=7.5\)
Definition: Mean
The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.
To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. \(7+9+12+13+14=55\) and \(55\div 5=11\).
Practice
Exercise \(\PageIndex{4}\)
A preschool teacher is rearranging four boxes of playing blocks so that each box contains an equal number of blocks. Currently Box 1 has 32 blocks, Box 2 has 18, Box 3 has 41, and Box 4 has 9.
Select all the ways he could make each box have the same number of blocks.
- Remove all the blocks and make four equal piles of 25, then put each pile in one of the boxes.
- Remove 7 blocks from Box 1 and place them in Box 2.
- Remove 21 blocks from Box 3 and place them in Box 4.
- Remove 7 blocks from Box 1 and place them in Box 2, and remove 21 blocks from Box 3 and place them in Box 4.
- Remove 7 blocks from Box 1 and place them in Box 2, and remove 16 blocks from Box 3 and place them in Box 4.
Exercise \(\PageIndex{5}\)
In a round of mini-golf, Clare records the number of strokes it takes to hit the ball into the hole of each green.
\(2\qquad 3\qquad 1\qquad 4\qquad 5\qquad 2\qquad 3\qquad 4\qquad 3\)
She said that, if she redistributed the strokes on different greens, she could tell that her average number of strokes per hole is 3. Explain how Clare is correct.
Exercise \(\PageIndex{6}\)
Three sixth-grade classes raised $25.50, $49.75, and $37.25 for their classroom libraries. They agreed to share the money raised equally. What is each class’s equal share? Explain or show your reasoning.
Exercise \(\PageIndex{7}\)
In her English class, Mai’s teacher gives 4 quizzes each worth 5 points. After 3 quizzes, she has the scores 4, 3, and 4. What does she need to get on the last quiz to have a mean score of 4? Explain or show your reasoning.
Exercise \(\PageIndex{8}\)
An earthworm farmer examined two containers of a certain species of earthworms so that he could learn about their lengths. He measured 25 earthworms in each container and recorded their lengths in millimeters.
Here are histograms of the lengths for each container.
- Which container tends to have longer worms than the other container?
- For which container would 15 millimeters be a reasonable description of a typical length of the worms in the container?
- If length is related to age, which container had the most young worms?
(From Unit 8.2.5)
Exercise \(\PageIndex{9}\)
Diego thinks that \(x=3\) is a solution to the equation \(x^{2}=16\). Do you agree? Explain or show your reasoning.
(From Unit 6.3.4)


5.4: Comparison and Patterning
Course Competency 5. Examine strategies that teach early math skills.
5.4. use attributes and objects for comparison and patterning.
Algebraic Thinking
Before reading this section, did you think that algebra was something that should be considered in the preschool classroom? Why or why not?
As with Geometry, one might think Algebra is too difficult of a subject for young children. However, early skills in comparison, patterning, and explaining thinking when combining sets (addition) or decomposing sets (subtraction) lay a strong foundation for algebraic thinking." The Wisconsin Model Early Learning Standard that aligns most closely with Algebraic Thinking is B.EL. 4 Uses the attributes of objects for comparison and patterning .
What is algebraic thinking?
As you read the Kansas Mathematics Standards, you will notice the Domain “Operations and Algebraic Thinking” in all grade levels preK grade 12. Furthermore, algebraic thinking and concepts permeate all areas of mathematics. Algebra is more than manipulating symbols or a set of rules, it is a way of thinking . When looking at the Wisconsin Standards for Mathematics, you will also see that standards for Algebraic Thinking are present in all grade levels K-12.
According to the K-5 Progression on Counting & Cardinality and Operations & Algebraic Thinking (2011), algebraic thinking begins with early counting and telling how many in a group of objects, and builds to addition, subtraction, multiplication, and division. Operations and Algebraic Thinking is about generalizing arithmetic and representing patterns .
Algebraic thinking includes the ability to
recognize patterns,
represent relationships,
make generalizations,
and analyze how things change.
In the early grades, students notice, describe, and extend patterns; and they generalize about those patterns.
Completing puzzles in preschool can indirectly relate to algebraic thinking by fostering foundational skills that are important for later mathematical concepts. Here's how:
1. **Pattern Recognition:** Many puzzles require children to identify and match patterns. This skill is fundamental in algebra, where recognizing patterns in numbers and operations is crucial.
2. **Problem-Solving:** Solving puzzles encourages critical thinking and problem-solving skills. These skills are transferrable to algebra, where students must analyze problems and develop strategies to find solutions.
3. **Spatial Reasoning:** Some puzzles, especially geometric puzzles, enhance spatial reasoning abilities. Spatial reasoning is important in algebraic thinking, especially when dealing with graphs and spatial representations of mathematical concepts.
4. **Logical Thinking:** Puzzles often require logical thinking and deduction. This logical approach is valuable in algebra, where students must follow logical steps and rules to solve equations and problems.
While completing puzzles directly addresses skills like pattern recognition and problem-solving rather than specific algebraic concepts, these foundational skills play a role in preparing children for more advanced mathematical thinking, including algebra, as they progress through their education. (OpenAI. (2024, May 10). Completing puzzles in preschool can indirectly relate to algebraic thinking [Response to "Does completing puzzles in preschool relate to algebra?"]. OpenAI. https://openai.com )
Connecting Number and Operations and Algebraic Thinking
Kindergarten
Students in kindergarten solve addition and subtraction problems in various ways as they make sense of and understand the concepts of addition and subtraction. Kindergarten students should see addition and subtraction equations, and should be encouraged to write equations, such as 4 + 3 = 7 and 7 – 3 = 4, but do not require this of students at this level. It is critical that students see the relationship between numbers, and teachers need to provide students those experiences to manipulate numbers using objects, drawings, mental images, etc. so that students can progress from the concrete, to the pictorial, to the abstract levels.
Preschool
Preschool teachers can connect number and operations to algebraic thinking in several ways:
1. **Pattern Recognition:** Introduce children to patterns in numbers and shapes. For example, use simple sequences like 1, 2, 3, 4, and encourage children to predict the next number. This lays the groundwork for understanding number sequences and algebraic patterns later on.
2. **Problem-Solving with Numbers:** Present age-appropriate word problems that involve basic addition and subtraction. Encourage children to use strategies like drawing pictures or using objects to solve these problems. This helps develop problem-solving skills, which are essential in algebra.
3. **Exploring Equality:** Teach children about the concept of equality using balance scales or visual representations. For instance, show that 2 + 3 is equal to 5 and explore different ways to represent this equation (e.g., 3 = 5 - 2). This introduces the idea of balancing equations, a fundamental concept in algebra.
4. **Introduce Variables:** Introduce the concept of variables using simple symbols (e.g., using a star "*" to represent an unknown quantity). Encourage children to solve problems where they need to find the value of the variable, such as in simple equations like 3 + * = 5.
5. **Use Concrete Manipulatives:** Utilize physical objects like blocks or counters to represent numbers and operations. This hands-on approach helps children understand abstract concepts by making them more tangible and relatable.
6. **Encourage Mathematical Discussions:** Foster discussions about mathematical concepts during group activities or circle time. Ask open-ended questions that promote critical thinking and reasoning, such as "How do you know that 2 + 2 is equal to 4?"
7. **Incorporate Math into Everyday Activities:** Find opportunities to integrate math into daily routines, such as counting during snack time or incorporating math concepts into storytelling or games.
By incorporating these strategies into their teaching practices, preschool teachers can effectively bridge the gap between number and operations and the foundational concepts of algebraic thinking, setting a strong foundation for future mathematical learning. (OpenAI. (2024, May 10). How preschool teachers can connect number and operations to algebraic thinking [Response to "How can preschool teachers connect number and operations to algebraic thinking?"]. OpenAI. https://openai.com )
Supporting Algebra and Functions (Classification and Patterning)
The information below is from the California Preschool Standards and is again provided as a reference to the age you may see these algebraic thinking skills appear. However, remember the Wisconsin Model Early Learning Standards include the skills for comparison and patterning in order of development but do not assign a specific age to any skills as all children develop at their own rate and time. The standards for Wisconsin emphasize that children should develop skills in categorizing, matching, sorting, using positional words, and patterning. See WMELS B.EL. 4 Uses the attributes of objects for comparison and patterning
Examples in 1.0 and 2.0 would correlate to WMELS B.EL. 4 Uses the attributes of objects for comparison and patterning.


1.1: College Research and Information Literacy
Why This Book?
The key to success in college research is to develop and hone your information literacy skills. These skills will prepare you to find and use information not only for college, but also in the workplace and your personal life. Having strong information literacy skills will make you a more thoughtful and effective consumer and creator of information, and will increase your awareness of and resilience toward the psychological, physiological, and sociological effects of living in a society overloaded with information.
“Recent events underscore the threat that digital illiteracy poses to public health and democracy” (Breakstone et al.).
What is Information Literacy?
Some of the skills and abilities that fall under the umbrella of information literacy include:
- research skills
- critical thinking
- media literacy
- digital literacy
- news literacy
- algorithmic literacy
- ethical reasoning
- civic engagement
Information literacy acknowledges that students are not just passive consumers of knowledge, but that you are active creators and participants in the information environment. It is a set of skills that aims to help students navigate this landscape, “not just for college courses but beyond —in the workplace, in their personal lives, as lifelong learners, and as news consumers, creators, and voters” (Head et al. 12; emphasis added).
You might also hear this idea referred to as “information competency,” which is an equivalent term.
“Information literacy is an integrated set of skills, knowledge, practices, and dispositions that prepares students to discover, interpret, and create information ethically while gaining a critical understanding of how information systems interact to produce and circulate news, information, and knowledge” (Head et al. 8).
National & International Perspectives
In the U.S., the Obama administration made information literacy a priority. The 2009 “Presidential Proclamation on National Information Literacy Awareness Month” stated that:
Over the past decade, we have seen a crisis of authenticity emerge. We now live in a world where anyone can publish an opinion or perspective, whether true or not, and have that opinion amplified within the information marketplace. At the same time, Americans have unprecedented access to the diverse and independent sources of information, as well as institutions such as libraries and universities, that can help separate truth from fiction and signal from noise….The ability to seek, find, and decipher information can be applied to countless life decisions, whether financial, medical, educational, or technical.
Internationally, the Alexandria Proclamation of 2005 defined the term as a human rights issue: “Information Literacy lies at the core of lifelong learning. It empowers people in all walks of life to seek, evaluate, use and create information effectively to achieve their personal, social, occupational and educational goals. It is a basic human right in a digital world and promotes social inclusion in all nations.”
“Information literacy is the set of integrated abilities encompassing the reflective discovery of information, the understanding of how information is produced and valued, and the use of information in creating new knowledge and participating ethically in communities of learning” (“Framework for Information Literacy for Higher Education”).
Sources
“ Beacons of the Information Society: The Alexandria Proclamation on Information Literacy and Lifelong Learning .” IFLA , 26 Jan. 2015.
Breakstone, Joel, et al. “ Lateral Reading: College Students Learn to Critically Evaluate Internet Sources in an Online Course .” Harvard Kennedy School Misinformation Review , vol. 2, no. 1, 2021, doi.org/10.37016/mr-2020-56. Licensed under CC BY 4.0
“ Framework for Information Literacy for Higher Education ” by the Association of College & Research Libraries is licensed under CC BY-NC-SA 4.0
Head, Alison J., Barbara Fister, and Margy MacMillan. “ Information Literacy in the Age of Algorithms .” Project Information Literacy , 15 Jan. 2020. Licensed under CC BY-NC-SA 4.0
Image: “ Digital Silhouette ” by Su San Lee is in the Public Domain, CC0
Image: “ Earth from Space ” by NASA is in the Public Domain, CC0
Image: “ Umbrella ” by Vectors Market , adapted by Aloha Sargent , is licensed under CC BY 4.0
“ Presidential Proclamation: National Information Literacy Awareness Month ” by Barack Obama is in the Public Domain.


5.4.1: Virulence Factors that Promote Colonization
Virulence factors are molecules expressed and secreted by that enable them to colonize the host, evade or inhibit the immune responses of the host, enter into or out of a host cell, and/or obtain nutrition from the host. The following are virulence factors that promote bacterial colonization of the host .
1. The ability to use motility and other means to contact host cells and disseminate within a host.
2. The ability to adhere to host cells and resist physical removal.
3. The ability to invade host cells.
4. The ability to compete for iron and other nutrients.
5. The ability to resist innate immune defenses such as phagocytosis and complement.
6. The ability to evade adaptive immune defenses.
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- <IP_ADDRESS>: The Ability to Use Motility and Other Means to Contact Host Cells
- Bacteria have to make physical contact with host cells before they can adhere to those cells and resist being flushed out of the body. Motile bacteria can use their flagella and chemotaxis to swim through mucus towards mucosal epithelial cells. Because of their thinness, their internal flagella (axial filaments), their corkscrew shape, and their motility, certain spirochetes are more readily able enter lymph vessels and blood vessels and spread to other body sites.
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- <IP_ADDRESS>: The Ability to Adhere to Host Cells and Resist Physical Removal
- One of the body's innate immune defenses is the ability to physically remove bacteria from the body. Bacteria may resist physical removal by producing pili, cell wall adhesin proteins, and/or biofilm-producing capsules that enable bacteria to adhere to host cells. At the end of the shaft of a bacterial pilus is an adhesive tip structure having a shape corresponding to that of specific receptor on a host cell for initial attachment. Bacteria can typically make a variety of different adhesive tips
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- <IP_ADDRESS>: The Ability to Evade Adaptive Immune Defenses
- There are various ways that the antibodies the body makes during adaptive immunity protect the body against bacteria. Some antibodies such as IgG and IgE function as opsonins and stick bacteria to phagocytes (opsonization or enhanced attachment). Antibodies, such as IgG, IgA, and IgM, can bind to bacterial adhesins, pili, and capsules and in this way block their attachment to host cells.


1.11: Last Great Glaciation
Movements of continents in this epoch led to very adverse consequences. Panama and Suez isthmus closed, Antarctica gradually shifted to the area of the South Pole, and the northern continents surrounded the Arctic region as a ring. Everything now was ready for new Great Glaciation .
Life in the seas has not changed much. At the beginning of the epoch, due to the dryer climate and the progressive development of herbivorous mammals, grasslands were extensively expanded. These areas were inhabited by a fauna in which various proboscis, ungulates, rodents, and predatory mammals dominated.
One of the most curious episodes of this era was the Great Inter-American Exchange , the result of the formation of the Panama Isthmus. South America, isolated so far from all other continents (like Australia now), experienced the invasion of more advanced North American groups. Some South American animals have successfully withstood this onslaught and even advanced far to the north (opossums, armadillos, porcupines). However, the more significant part of the South American fauna went extinct.
After the formation of the glaciers, the rich Antarctic fauna and flora also died out, the last remnants (refugia) of which are now in the remnants of flooded Zealandia continent: now islands New Zealand, Lord Howe, and New Caledonia.
The advent of the glacier led to the formation of another type of community, arctic steppe : tundra , which advanced or retreated along with the ice.
The final accord of the development of the biosphere in this era was the appearance (most likely in East Africa) of representatives of the species Homo sapiens L.


8.4: Moral Culpability versus Legal Culpability
Moral culpability is loosely tied to mens rea, meaning that there is an explanation for the intent of the actor. However, with moral culpability, the explanation put forth by the actor may excuse the immoral action from being caused due to intentional immorality. An example would be a mother who has killed her infant while suffering postnatal depression. The mother would not be charged with murder, as would a stranger who killed the same infant, or a mother who is not suffering postnatal depression who killed her infant. However, because the mother suffers from a medical diagnosis of postnatal depression, she would be charged with the lesser offence of infanticide.  A further example would be a person who kills someone because he threatened serious bodily harm to another person. Although the action is homicide, there may be no moral culpability because the intent was first to save another person even though the mens rea may have existed to kill the victim in order to stop him. Because the moral culpability is less than if someone killed for his or her own gain, a manslaughter charge would be used instead of a murder charge. Here we weigh moral culpability against legal culpability .
A police officer on the street may, in some instances, use his or her discretion when determining moral culpability or legal culpability for minor investigations. Where a suspect of a crime may be charged with an offence, the officer may decide not to charge because of diminished moral culpability. An example is a minor theft in which a homeless suspect steals a blanket in order to survive a frigid night on the streets. The officer may choose to forgo charges and locate a shelter for the homeless suspect.
The distinction between moral culpability and legal culpability is at times blurred; law enforcement officers must be aware that what may be legally permissible may not be morally permissible. While it is true that in solving ethical dilemmas, officers should consider the laws or regulations that are applicable, so too must they consider the moral culpability in all their actions regardless of the lack of legal restrictions. An example in a law enforcement context may be an officer who ignores a homeless person waving her hand for assistance. While there may be no policy or legal infraction, the officer’s conduct may be regarded as morally culpable if the homeless person is later harmed when the officer’s assistance may have protected her from harm. The officer who ignored the person may be regarded as morally culpable for the injury by not assisting the person. Another example would be an officer who fails to investigate a crime due to a heavy caseload. Should the omission of the investigation lead to a preventable assault, the argument may be made that the investigator’s decision not to investigate made him or her morally culpable, depending on the reasoning behind the officer’s decision. If the officer decided that the case was not as serious as others, then it may be determined that the officer was not morally culpable. However, if the officer’s decision was based upon the ethnicity of the victim, then the officer would be morally culpable for the assault that occurred as a result of the officer’s decision.


1.1: Why Should I Care About The Law?
Introduction
If you are like a number of undergraduate business students, you might initially see a “law class” as just another course you have to take because it is required for your major. You might be thinking, "I'm going into the business world, not the law," or "We don't really need to know this because we can leave the law to the lawyers." But that mindset presents a couple of practical problems. First, the law is an integral component of most business decisions. Whether planning or executing business decisions—or responding to those of others—some aspect of the law tends to be a factor necessary to sound decision-making. Second, businesses cannot simply "leave the law to the lawyers" because a lawyer cannot be with every decision-maker all the time. (Of course, no one would want that.)
Certainly, this class is not a law school course, and it is not about turning students into lawyers. On the other hand, this class may feel like a mini-law school course because how lawyers think and how adept business professionals need to think are more similar than many people might believe. In fact, there is an entire book written about it: Think Like a Lawyer: Legal Reasoning for Law Students and Business Professionals . [1]
The significance of legal thinking in business activities and relations cannot be overstated because legal risk plays a substantial role in a business's bottom line. [2] Referring to undergraduate students, Professor Jooho Lee of Pepperdine University’s business school advised that:
[L]egal reasoning skills improve their ability to identify and isolate relevant information from irrelevant information, think comprehensively, and communicate their ideas clearly and concisely. These skills are important not only for business but also for good citizenship and a flourishing life. [3]
Of course, professors typically have some bias of about the importance of their courses, so, let's hear from the professionals. In a risk management study, C-level executives (CEOs, CFOs, etc.) across nine industries and 446 organizations ranked Legal Risks as their top external pressure . [4] :
In a recent Travelers Business Risk Index survey of more than 1,200 business risk managers, only two categories were among the top ten risks in every industry: legal liability and medical cost inflation. Another category of legal risk, complying with laws, was in the top ten for nine of the ten industries studied. [5]
The key role that legal considerations play in management is further demonstrated in a survey of over 900 senior managers and executives attending executive programs at the University of Michigan, which showed that they took more sessions on law than any other, aside from Organizational Behavior and Finance. [6] (Presumably, they did not take the legal sessions for amusement but instead for their added value.)
Legal concerns do not just affect senior management and executives; they are also inherent in other decision-making roles. For example:
A recent Corporate Executive Board Legal Leadership Council survey concluded that middle managers make 75 percent of legal decisions and that almost 80 percent of corporate employees made a decision or completed an activity with a significant legal implication in the past year. These middle-management decisions involved, for example, signing contracts, developing new products, creating intellectual property, interacting with government officials, entering new markets, creating marketing materials, establishing product safety standards, and executing acquisition agreements. Fewer than one-third of these middle managers consulted the legal department when making their decisions. In other words, they relied on their own knowledge of the law when making everyday business decisions, which are usually intertwined with legal concerns. [7]
Understanding the rules allows managers to compete in competitive markets and to make judgments about political and business risks. [8] Law can be used in ways to allow managers to compete. A common perspective is a perception that risk management helps prevent losses: “We can do this, but we can’t do that.” However, while understanding the law helps mitigate losses, managers also need to see managing legal risk as a way to create business opportunities and value.
Leaders create opportunity and value by being legally shrewd.
Managers need to "possess legal astuteness and regard the law as a key enabler of value creation. [9] Ultimately, managers who can bridge business strategy and the law give businesses opportunities to create a competitive advantage in the market. This advantage results from being educated about the law and understanding how the law ought to factor in strategic decision-making.
Decision-making is one of a manager’s four major roles. [10] Drilling down, managers play four basic decision-making roles: Entrepreneur, resource allocator, disturbance handler, and negotiator. [11] Legal issues pervade entrepreneurial and resource allocation activities because they deal with issues like developing projects, departmental reorganizations, developing marketing plans, entrusting others with executing strategies and decisions, public relations, mergers and acquisitions, and more. [12]
As negotiators, managers spend substantial time working on contractual relationships and committing resources to them. [13] As disturbance handlers, managers involuntary address circumstances beyond their control, rapidly developing pressures of situations that “are too severe to be ignored,” such as suppliers breaching contracts. [14] Other examples include reports of discriminatory termination, sexual harassment, and injuries caused by employees, and communications with legal counsel and stakeholders. [15]
Moreover, those starting businesses make decisions about:
- the legal form of their business;
- government regulations that govern how they develop and market products and services;
- liability risks in manufacturing and selling their products;
- protection of their intellectual property;
- the nature of their contracts with customers and suppliers;
- legal considerations relating to financing the business; and
- the law that governs hiring employees. [16]
Therefore, Ladwig & Siedel identify seven management skills that are critical for business success :
- The ability to recognize legal issues that arise daily;
- The ability to decide which legal issues require seeking legal advice;
- The ability to communicate effectively with legal advisors;
- The ability to evaluate legal advice;
- The ability to implement legal decisions;
- The ability to discuss legal issues with stakeholders; and
- The ability to lead by highlighting the legal responsibilities of those within the organization. [17]
The goal of this introduction to the law is to help build a foundation on which these seven skills can grow.
Notes
- (Boldface added.) Fruehwald, E. S. (2020). Think like a lawyer: Legal reasoning for law students and business professionals (2nd ed.). Amazon Digital Services LLC. (Note: Readers can access the first edition of this book for free at the Internet Archive .)
- Siedel, G. J. (2017, March 15). Law and the business school curriculum . AACSB International.
- Learning business law: 8 things students should know before entering the workforce . (2023, November 21). Stukent.
- Accenture. (2013). Global risk management study: risk management for an era of greater uncertainty .
- See note 2.
- Ladwig, C., & Siedel, G. (2020). Strategy, Law and Ethics for Business Decisions. West Academic.
- See note 2.
- Hotchkiss, C. (1994). International Law for Business. McGraw-Hill.
- See note 6.
- Mintzberg, H. (1990). The manager’s job: Folklore and fact . Harvard Business Review.
- See note 11.
- Ladwig & Seidel, supra ; Mintzberg, supra .
- See note 11.
- See note 11.
- See note 13.
- See note 6.
- See note 6.


12.2: Ecology of Vegetation and Plant Succession
Principal Adaptive Strategies of Vegetation
Plants evolve a variety of adaptations to the light and moisture availability within a particular environment in order to flourish. Plants adaptations include those of leaf form and canopy structure (the roof of foliage formed by the crowns of trees). For instance, a hard, needle leaf structure is an adaptation to extreme temperatures and low moisture status in winter. The leaves of some rain forest trees have a special joint at the bottom of their stalk that enables them to twist and turn to follow the light as the sun passes from east to west over head. Deciduous trees drop their leaves to cut transpiration loss during dry periods and when temperatures are very cold.
Conifer needles are an important adaptation to the extreme conditions present in the climate of the boreal forest. Pine needles contain very little sap, so freezing is not much of a problem. Conifer needles have a unique structure which limits the loss of water, a precious commodity in this environment. Pine needles have fewer stomata than broadleaf tree leaves. The stomata are recessed into pits on the needle and aligned in a groove on its underside. The groove in the needle creates a small layer of still air which slows the loss of water vapor by diffusion. Water loss is further reduced by the thick waxy coating common to pine needles. Water is "shut off" from the tree when the ground completely freezes. Under these circumstances the stomata close-up to prevent loss of water from the tree.
Fleshy "leaves", like those of desert succulents or thick skin like that of the giant Saguaro cactus helps retain moisture. The Baobab tree, found in the wet/dry tropical (savanna) climate stores water in its trunk to combat the long drought period experienced in that climate.
Plants have adapted particular root structures to live in arid regions. Deep tap roots draw moisture hidden deep below the surface while extensive near - surface root systems catch moisture as it infiltrates into soil. The Havard Oak (Figure 12.*) is a shrub found in the semi-arid southwestern United States. It is well adapted to the dry conditions having an extensive root system and tap roots that extend 15 to 20 feet deep. Tap roots " equal to a man's thigh " are not uncommon. Above ground, thick waxy leaves reduce water loss through transpiration.Some desert grasses have rolled surfaces to reduce water loss from the inner surface and hairs which reduce air movement.
Canopy structures reflect the environmental conditions vegetation grows in. The conical canopies of conifers help shed snow and catch low angle sun rays during the long winters where they grow. The rain forest displays a multi-layered canopy. Each layer possesses organisms adapted to the environmental conditions found in it. A canopy can be so thick and dense, like that found in the rain forest, that little light penetrates to the surface. The lack of light for understory growth creates an open forest structure that you can see into for some distance. Where canopy density is low, more light filters to the surface creating a thick ground cover and a closed forest structure . Standing on the floor of a closed forest, it's nearly impossible to see more than a few meters into it.
Plant Communities
Rarely is any location dominated by a single specie of plant. A plant community refers to the associated plant species that form the natural vegetation of any place. For instance, a midlatitude forest is comprised of a community of trees, shrubs, ferns, grasses, and flowering herbs. Plant communities provide a habitat for animals and significantly modify the local environment. Plant communities affect soil type when organic material decomposes into the soil altering soil moisture retention, infiltration capacity, soil structure and soil chemistry. Trees shade the forest floor, reducing incident solar radiation and lowering temperatures of both the soil and the air. Reduced incident light decreases evaporation keeping soils moister beneath the forest canopy. These impacts affect animal habitats and the diversity of animal species which are associated with these plant communities.
An ecotone is a plant community in a distinct zone of transition between other more extensive communities. Ecotones vary in scale, from local (between forest and field) to global (savannas). Within an ecotone plants of different environmental tolerances often intermingle. For instance, grasses adapted to low moisture conditions intermingle with deciduous trees within a prairie - forest ecotone.
Plant Succession
Natural vegetation of a particular location evolves in a sequence of steps involving different plant communities. The evolutionary process is known as plant succession . Plant succession usually begins with a fairly simple community known as a pioneer community . The pioneer community, and each successive community alters the environment in such a way to permit new communities to occupy a site. These alterations of the environment include changes in site microclimate and soil conditions.
A climax community is the result of a long period of plant succession. Climax communities usually exhibit a good deal of species diversity and thus are relatively stable systems. Disturbance renews a successional sequence. Plant succession was renewed after the explosion of Mt. St. Helens with the subsequent disruption of biotic communities that inhabited the region. Human disturbance related to tropical deforestation has renewed the successional sequence of plant communities in the tropical rain forest.
Video : "Climax Communities Are Largely Stable" (Courtesy of Great Pacific Media)


2.5: Current Assets - Inventory and Accounts Receivable
The accountant defines the word, “current,” as in “current asset” – or “current liability” – as an item, which is consumed or exhausted within one calendar year. On the balance sheet, we observe numerous such assets and liabilities. For example, inventory is held by the corporation for sale in the near future and, presumably, is sold in less than one year (in most instances). In fact, the sooner the corporation disposes of its inventory the better, by and large.
“Accounts receivable” is a current asset that bears some further explanation. In many instances, a customer pays for goods purchased at the point of sale. He receives the goods (i.e., the corporation’s inventory) and pays at the same time.That is what usually happens when consumers buy goods at the store. At the time of (a “cash”) sale, the seller reduces inventory (credit) and increases cash (debit).
In many, if not most, large business transactions, the customer may receive the goods, but not pay for them until later. The seller may grant the customer “credit” for the purchase and require “terms of sale” to which the buyer agrees. The terms of sale will dictate that the customer pay for the goods, typically, but not always, within thirty days of delivery. This sale would be referred to as a “credit sale” rather than a “cash sale,” and would be indicated as such on the company’s income statement (see below).
At the time of the credit sale, the seller will record, or “book,” an account receivable for the sale on its balance sheet, while the buyer will book an account payable on its. Simultaneously, the seller reduces (i.e., credits) his inventory and the buyer increases (i.e., debits) his.
When payment is made, the accounts receivable are adjusted (as will the cash account). In the case of the seller, the account receivable is reduced (i.e., credited) and the cash account will be increased (i.e., debited).
In the case of the buyer, the account payable will be reduced (i.e., debited) and cash will be reduced (i.e., credited) as well.


3.3: Assignment- Mission Impact on Business Practice and Employee Behavior
Preparation
Our text introduced a number of foundational business management concepts and related terminology. The module also discussed the operational significance of these concepts. In this exercise, you will have an opportunity to explore the way an organization’s mission, vision and values influence their business practices and employee behavior—or not!
Your Task
- Select a business or organization that you’re familiar with and conduct research to determine their stated mission, vision and values.
- Reflect on your experience with the company/organization. Do the statements ring true or hollow? That is, do their business practices reflect the stated mission, vision and values?
- Write a brief post identifying your selected organization’s mission, vision and values and your opinion on the validity of the statements. Support your position with a specific example based on your personal experience or research. As always, include links to sources cited.
Contributors and Attributions
CC licensed content, Original
- Assignment: Mission Impact on Business Practice and Employee Behavior. Authored by : Nina Burokas. Provided by : Lumen Learning. License : CC BY: Attribution


17: Appendices Last updated Save as PDF Page ID 10828 Paul Pfeiffer Rice University 17.1: Appendix A to Applied Probability- Directory of m-functions and m-procedures 17.2: Appendix B to Applied Probability- some mathematical aids 17.3: Appendix C- Data on some common distributions 17.4: Appendix D to Applied Probability- The standard normal distribution 17.5: Appendix E to Applied Probability - Properties of Mathematical Expectation 17.6: Appendix F to Applied Probability- Properties of conditional expectation, given a random vector 17.7: Appendix G to Applied Probability- Properties of conditional independence, given a random vector 17.8: Matlab files for "Problems" in "Applied Probability"


2.1.4: Size and Shape
Those involved in the study of measuring the Earth, called geodesists , don't know exactly what the true shape of the Earth is. We often describe it as a sphere but it's more like an oblate spheroid . That is, Earth is wider in the middle and flatter at the poles than a perfect sphere. From pole-to-pole the distance is 12,713.6 km. The equatorial diameter Earth is about 7926 miles (12,756 km) while the polar diameter is 7900 miles (12,714 km). The equatorial circumference is approximately 24,900 miles (40,075 km). The equatorial bulge is due to the centrifugal force exerted on the Earth by its rotation.
On December 26 th , 2004 subduction occurred between the India and Burma plates off the coast of Indonesia making for a slightly more compact Earth. The shift in Earth's crust resulted in a magnitude 9 earthquake and large tsunami that devastated South Asia . Interestingly, Earth became slightly more round and the North Pole shifted by about 2.5 cm (an inch) in the direction of 145 degrees East longitude (Science Daily, 2005).
From the top of Mt. Everest at 29,029 feet (8848 m) in the Himalayas, to the depths of the Mariana Trench in the Pacific at 36,198 feet (11,033 meters) below sea level, Earth has a total relief of about 12 miles. Though this seems to be a great distance, it's a mere blip when compared to the diameter of Earth.


10.2: Measuring and Reducing Poverty
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Since the end of the Second World War states have come together to find ways to reduce poverty through prompting economic growth. As discussed earlier in the chapter, concepts of global justice underpin international poverty-reduction strategies, giving focus to approaches that seek to enhance the rights of the marginalised. The extent to which these efforts have been successful is highly debatable – but the intent has certainly been there. States have attempted to address the challenges of poverty at a global level in various ways. We discuss four approaches below.
1. Official development assistance (aid)
Typically, aid comes from developed states and is either channelled bilaterally (or directly) from one state to another or diverted multilaterally through international organisations like the United Nations. It is one way in which wealthy nations have attempted to meet their moral obligation to assist poorer nations. Indeed, developed countries have spent a great deal on official development assistance over the years. In 2014 alone, states spent over $135bn on aid according to a report from the Organisation for Economic Cooperation and Development (OECD). However, the success of such efforts has been inconsistent, and in some cases poverty has actually got worse. The reasons for this are complex but some examples may be helpful.
First, inappropriate types of aid can be sent. Instead of sending money that a developing country can use to address poverty, developed states sometimes provide goods that may or may not be helpful. For example, in Gambia a number of oxygen devices were donated to a hospital, but unfortunately they were not compatible with the local electricity voltage. This rendered the devices unusable, highlighting how aid needs to be properly thought through. Second, corruption in some countries has seen aid syphoned off into the offshore bank accounts of the political elite. For example, the New York Times claimed that over $1 billion in foreign aid intended to help Bosnia rebuild itself after years of destructive war was stolen by Bosnian officials for personal gain (Hedges 1999).
Aid has also been used for the political purposes of the providing state. For example, during the Cold War the United States and the Soviet Union used aid to prop up states that were sympathetic to their own political cause. In many of those places this did little to address poverty; rather, it helped fund regional wars that led to further instability and poverty. For example, the 1975–2002 civil war in Angola saw the Soviet Union and the United States provide aid in the form of military assistance to opposing forces. Aid has also come from developed countries or international institutions with specific conditions for use (‘conditionalities’) that have only served to make things worse. As already mentioned, such aid requires the receiving nation to restructure its economy in ways that may not benefit the most vulnerable people. For example, during the structural adjustment programmes of the 1980s in Latin America, income per capita fell in 18 countries. During similar programmes in sub-Saharan Africa, income per capita fell in 26 countries over the same period (Stewart 1991).
2. Trade and investment
The trade in goods and services together with foreign direct investment by private corporations can play an important role in poverty reduction. One of the ideas behind free trade and reducing barriers to investment between countries is to provide opportunity for states in the international system to grow economically. International trade in goods and services has risen significantly since 1945. Investment between states, or so-called foreign direct investment, has been a major source of that economic growth. But these global activities frequently hide an inconvenient reality: developing countries are often only involved in a minor way in global trade and investment activities. This is due to a number of reasons ranging from inadequate infrastructure such as roads, rail, and ports to limited access to financial capital. In comparison to developed nations, many developing countries have a higher proportion of lower skilled or undereducated workers in their workforce. As a result, investment opportunities that require highskilled and high-income employment are more often found in developed countries and investment by corporations in developing nations typically targets a low-skilled and low-wage workforce. This reality is difficult to overcome. Although nations such as China and India are investing heavily in an attempt to level the playing field, they are more fortunate than others due to their comparative wealth and high historic levels of economic growth. Despite some notable exceptions, the general picture is that trade and investment have not assisted poverty reduction to any significant extent.
3. Money lending
A third poverty-reducing strategy is lending developing countries money, or capital, so that they can invest in areas that will help them develop economically. Money lending is different from aid as loans need to be paid back, with interest. Loans can be provided for key infrastructure projects like bridges, roads, electricity lines and power plants. These can typically act as catalysts for economic development, but they require significant access to capital. The importance of access to capital resulted in the establishment of the World Bank in 1944. Its mission was to lend developing countries money at below market interest rates and also provide expert advice on the establishment of sound economic policies. On paper, the idea is a good one. However, the practices of the World Bank are not without controversy. As we explored earlier in the chapter, there has been criticism of the conditions attached to the loans. Although the most censured of the policies have been abandoned, damage has been done. In addition, the provision of interestbearing loans to developing countries has created a huge problem of indebtedness. Many developing countries cannot afford to invest in important domestic programmes such as education and healthcare due to the burden of their debt repayments. This has sparked calls to cancel the debt of developing countries and allow them a fresh start. To date, although some debt has been cancelled, the larger challenges caused by the nature of outstanding loans and how they were imposed remain.
4. United Nations’ goals
In response to the many failings noted above, a new approach emerged in 2000 when the United Nations and its member states moved to eradicate extreme poverty by 2015. The United Nations Millennium Development Goals (MDGs) consisted of eight categories or areas of focus for states to engage in:
1. Eradicate extreme hunger and poverty
2. Achieve universal primary education
3. Promote gender equality and empower women
4. Reduce child mortality
5. Improve maternal health
6. Combat HIV/AIDS, malaria and other diseases
7. Ensure environmental sustainability
8. To develop a global partnership for development.
A cross-section of approaches was employed for achieving these goals, including harnessing elements of the three strategies outlined above. The key thing however, was to have a coordinated approach to a set of agreed targets. However, the initiative proved a mixed bag in terms of results. For example, some goals related to education and child mortality have seen real – if uneven – progress, while rates of hunger and malnutrition have actually worsened in some cases. Exacerbating this further, the aftermath of the 2008 financial crisis has reduced the projected amount of money (and jobs) available to many governments. Anthony Lake, Executive Director of the United Nations Children’s Fund (UNICEF), accounted for the mixed picture of success and failure as follows:
In setting broad global goals the MDGs inadvertently encouraged nations to measure progress through national averages. In the rush to make that progress, many focused on the easiest-to-reach children and communities, not those in greatest need. In doing so, national progress may actually have been slowed. (UNICEF, 2015)
Given these unsatisfactory results, the international community agreed that a more robust initiative was needed and the Sustainable Development Goals (SDGs) were adopted at the United Nations in 2015. They have 169 clear targets spread over 17 priority areas, all to be achieved by 2030:
1. No poverty
2. No hunger
3. Good health
4. Quality education
5. Gender equality
6. Clean water and sanitation
7. Renewable energy
8. Good jobs and economic growth
9. Innovation and infrastructure
10. Reduced inequalities
11. Sustainable cities and communities
12. Responsible consumption
13. Climate action
14. Life below water
15. Life on land
16. Peace and justice
17. Partnerships for the goals.
Like the Millennium Development Goals, the Sustainable Development Goals can be described as aspirational. Although the newer targets have their critics, one reason that they may offer greater hope in reducing poverty is that the planned interventions are more detailed. The target is not only reducing poverty, but addressing the many conditions that feed and cement conditions of poverty, including poor (or negative) economic growth. And the most vulnerable are now being targeted proactively, addressing one of the criticisms of the Millennium Development Goals.


1.5: Reconstruction and Women
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Reconstruction involved more than the meaning of emancipation. Women also sought to redefine their roles within the nation and in their local communities. The abolitionist and women’s rights movements simultaneously converged and began to clash. In the South, both black and white women struggled to make sense of a world of death and change. In Reconstruction, leading women’s rights advocate Elizabeth Cady Stanton saw an unprecedented opportunity for disenfranchised groups. Women as well as black Americans, North and South, could seize political rights. Stanton formed the Women’s Loyal National League in 1863, which petitioned Congress for a constitutional amendment abolishing slavery. 21 The Thirteenth Amendment marked a victory not only for the antislavery cause but also for the Loyal League, proving women’s political efficacy and the possibility for radical change. Now, as Congress debated the meanings of freedom, equality, and citizenship for former slaves, women’s rights leaders saw an opening to advance transformations in women’s status, too. On May 10, 1866, just one year after the war, the Eleventh National Women’s Rights Convention met in New York City to discuss what many agreed was an extraordinary moment, full of promise for fundamental social change. Elizabeth Cady Stanton presided over the meeting. Also in attendance were prominent abolitionists with whom Stanton and other women’s rights leaders had joined forces in the years leading up to the war. Addressing this crowd of social reformers, Stanton captured the radical spirit of the hour: “now in the reconstruction,” she declared, “is the opportunity, perhaps for the century, to base our government on the broad principle of equal rights for all.” 22 Stanton chose her universal language—“equal rights for all ”—with intention, setting an agenda of universal suffrage. Thus, in 1866, the National Women’s Rights Convention officially merged with the American Anti-Slavery Society to form the American Equal Rights Association (AERA). This union marked the culmination of the long-standing partnership between abolitionists and women’s rights advocates.
The AERA was split over whether black male suffrage should take precedence over universal suffrage, given the political climate of the South. Some worried that political support for freedmen would be undermined by the pursuit of women’s suffrage. For example, AERA member Frederick Douglass insisted that the ballot was literally a “question of life and death” for southern black men, but not for women. 23 Some African American women challenged white suffragists in other ways. Frances Harper, for example, a freeborn black woman living in Ohio, urged them to consider their own privilege as white and middle class. Universal suffrage, she argued, would not so clearly address the complex difficulties posed by racial, economic, and gender inequality. 24
These divisions came to a head early in 1867, as the AERA organized a campaign in Kansas to determine the fate of black and woman suffrage. Elizabeth Cady Stanton and her partner in the movement, Susan B. Anthony, made the journey to advocate universal suffrage. Yet they soon realized that their allies were distancing themselves from women’s suffrage in order to advance black enfranchisement. Disheartened, Stanton and Anthony allied instead with white supremacists who supported women’s equality. Many fellow activists were dismayed by Stanton’s and Anthony’s willingness to appeal to racism to advance their cause. 25
These tensions finally erupted over conflicting views of the Fourteenth and Fifteenth Amendments. Women’s rights leaders vigorously protested the Fourteenth Amendment. Although it established national citizenship for all persons born or naturalized in the United States, the amendment also introduced the word male into the Constitution for the first time. After the Fifteenth Amendment ignored sex as an unlawful barrier to suffrage, an omission that appalled Stanton, the AERA officially dissolved. Stanton and Anthony formed the National Woman Suffrage Association (NWSA), while suffragists who supported the Fifteenth Amendment, regardless of its limitations, founded the American Woman Suffrage Association (AWSA).
The NWSA soon rallied around a new strategy: the New Departure. This new approach interpreted the Constitution as already guaranteeing women the right to vote. They argued that by nationalizing citizenship for all people and protecting all rights of citizens—including the right to vote—the Fourteenth and Fifteenth Amendments guaranteed women’s suffrage. Broadcasting the New Departure, the NWSA encouraged women to register to vote, which roughly seven hundred did between 1868 and 1872. Susan B. Anthony was one of them and was arrested but then acquitted in trial. In 1875, the Supreme Court addressed this constitutional argument: acknowledging women’s citizenship but arguing that suffrage was not a right guaranteed to all citizens. This ruling not only defeated the New Departure but also coincided with the Court’s broader reactionary interpretation of the Reconstruction amendments that significantly limited freedmen’s rights. Following this defeat, many suffragists like Stanton increasingly replaced the ideal of universal suffrage with arguments about the virtue that white women would bring to the polls. These new arguments often hinged on racism and declared the necessity of white women voters to keep black men in check. 26
Advocates for women’s suffrage were largely confined to the North, but southern women were experiencing social transformations as well. The lines between refined white womanhood and degraded enslaved black femaleness were no longer so clearly defined. Moreover, during the war, southern white women had been called on to do traditional men’s work, chopping wood and managing businesses. While white southern women decided whether and how to return to their prior status, African American women embraced new freedoms and a redefinition of womanhood.
 Many did not like what they saw, especially given the possibility of racial equality. Formerly wealthy women hoped to maintain their social status by rebuilding the prewar social hierarchy. Through Ladies’ Memorial Associations and other civic groups, southern women led the efforts to bury and memorialize the dead, praising and bolstering their men’s masculinity through nationalist speeches and memorials. Ladies’ Memorial Associations (LMAs) grew out of the Soldiers’ Aid Society and became the precursor and custodian of the Lost Cause narrative. Proponents of the Lost Cause tried to rewrite the history of the antebellum South to deemphasize the brutality of slavery. They also created the myth that the Civil War was fought over states’ rights instead of slavery, which was the actual cause. LMAs and their ceremonies created new holidays during which white southerners could reaffirm their allegiance to the Confederacy and express their opposition to black rights. For instance, some LMAs celebrated the anniversary of Stonewall Jackson’s death on May 10. 27 Through these activities, southern women took on political roles in the South.
Southern black women also sought to redefine their public and private lives. Their efforts to control their labor met the immediate opposition of southern white women.  A misunderstanding quickly developed. The laundress, nameless in Gertrude’s records, performed her job and returned home. Gertrude believed that her money had purchased a day’s labor, not just the load of washing, and she became quite frustrated. Meanwhile, this washerwoman and others like her set wages and hours for themselves, and in many cases began to take washing into their own homes in order to avoid the surveillance of white women and the sexual threat posed by white men. 28
Similar conflicts raged across the South. White southerners demanded that African American women work in the plantation home and instituted apprenticeship systems to place African American children in unpaid labor positions. African American women combated these attempts by refusing to work at jobs without fair pay or fair conditions and by clinging tightly to their children.
Like white LMA members, African American women formed clubs to bury their dead, to celebrate African American masculinity, and to provide aid to their communities. On May 1, 1865, African Americans in Charleston created the precursor to the modern Memorial Day by mourning the Union dead buried hastily on a race track turned prison. 29 Like their white counterparts, the three hundred African American women who participated had been members of the local Patriotic Association, which aided freedpeople during the war. African American women continued participating in federal Decoration Day ceremonies and, later, formed their own club organizations. Racial violence, whether city riots or rural vigilantes, continued to threaten these vulnerable households. Nevertheless, the formation and preservation of African American households became a paramount goal for African American women.
 Southern women celebrated the return of their brothers, husbands, and sons, but couples separated for many years struggled to adjust. To make matters worse, many of these former soldiers returned with physical or mental wounds. For white families, suicide and divorce became more acceptable, while the opposite occurred for black families. Since the entire South suffered from economic devastation, many families were impoverished and sank into debt. All southern women faced economic devastation, lasting wartime trauma, and enduring racial tensions.


8.3: Future Value of Annuities and Sinking Funds
Learning Objectives
In this section, you will learn to:
- Find the future value of an annuity.
- Find the amount of payments to a sinking fund.
Prerequisite Skills
Before you get started, take this prerequisite quiz.
1. Solve \(24=6\cdot x^3\).
- Click here to check your answer
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\(x=\sqrt[3]{4}\approx1.5874\)
If you missed this problem, review here . (Note that this will open a different textbook in a new window.)
2. Solve \(24=6\cdot 3^x\).
- Click here to check your answer
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\(x=\log_3(4)\approx1.2619\)
If you missed this problem, review Section 7.3 . (Note that this will open in a new window.)
3. Simplify \(\dfrac{500(2-\dfrac{5}{6})^{5\cdot4}-1}{\dfrac{2}{3}}\) in your calculator.
- Click here to check your answer
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\(16,366.55426\)
If you missed this problem, review here . (Note that this will open a YouTube video in a new window.)
Ordinary Annuities
In the first two sections of this chapter, we examined problems where an amount of money was deposited as a lump sum in an account and was left there for the entire time period. Now we will do problems where timely payments are made in an account. When a sequence of payments of some fixed amount are made in an account at equal intervals of time, we call that an annuity . And this is the subject of this section.
Example \(\PageIndex{1}\)
If at the end of each month a deposit of $500 is made in an account that pays 8% compounded monthly, what will the final amount be after five years?
Solution
There are 60 deposits made in this account. The first payment stays in the account for 59 months, the second payment for 58 months, the third for 57 months, and so on. We can use the formula for compound interest to examine each payment.
- The first payment of $500 will accumulate to an amount of $500(1 + 0.08/12) 59 .
- The second payment of $500 will accumulate to an amount of $500(1 + 0.08/12) 58 .
- The third payment will accumulate to $500(1 + 0.08/12) 57 .
- The fourth payment will accumulate to $500(1 + 0.08/12) 56 .
And so on . . .
Finally the next to last (59 th ) payment will accumulate to \($500(1 + 0.08/12)^1\).
The last payment is taken out the same time it is made, and will not earn any interest.
To find the total amount in five years, we need to add the accumulated value of these sixty payments.
In other words, we need to find the sum of the following series.
\[\$ 500(1+0.08 / 12)^{59}+\$ 500(1+0.08 / 12)^{58}+\$ 500(1+0.08 / 12)^{57}+\ldots+\$ 500 \nonumber\]
Written backwards, we have
\[ \$500 +\$ 500(1+0.08 / 12)+\$ 500(1+0.08 / 12)^{2}+\ldots+\$ 500(1+0.08 / 12)^{59} \nonumber\]
This is a geometric series with \(a = $500\), \(r = (1 + 0.08/12)\), and \(n = 59\). The sum is
\[\begin{align*} \text{sum} &= \dfrac{\$ 500\left[(1+0.08 / 12)^{60}-1\right]}{0.08 / 12} \\[4pt] &=\$ 500(73.47686) \\[4pt] &=\$ 36,738.43 \end{align*}\]
When the payments are made at the end of each period rather than at the beginning, we call it an ordinary annuity .
Future Value of an Ordinary Annuity
If a payment of m dollars is made in an account n times a year at an interest \(r\), then the final amount \(A\) after \(t\) years is
\[\mathbf{A}=\frac{\mathbf{m}\left[(\mathbf{1}+\mathbf{r} / \mathbf{n})^{\mathbf{n} \mathbf{t}}-\mathbf{1}\right]}{\mathbf{r} / \mathbf{n}} \]
The final amount is also called the future value or the accumulated value.
Example \(\PageIndex{2}\)
Tanya deposits $300 at the end of each quarter in her savings account. If the account earns 5.75% compounded quarterly, how much money will she have in 4 years?
Solution
The future value of this annuity can be found using the above formula.
\[\begin{align*} A&=\frac{\$ 300\left[(1+.0575 / 4)^{16}-1\right]}{0.0575 / 4} \\[4pt] &=\$ 300(17.8463) \\[4pt] &=\$ 5353.89 \end{align*}\]
If Tanya deposits $300 into a savings account earning 5.75% compounded quarterly for 4 years, then at the end of 4 years she will have $5,353.89
Example \(\PageIndex{3}\)
Robert needs $5,000 in three years. How much should he deposit each month in an account that pays 8% compounded monthly in order to achieve his goal?
Solution
If Robert saves m dollars per month, after three years he will have
\[\dfrac{m\left[(1+.08 / 12)^{36}-1\right]}{0.08 / 12} \nonumber\]
But we'd like this amount to be $5,000. Therefore,
\[\begin{align*} \frac{\mathrm{m}\left[(1+.08 / 12)^{36}-1\right]}{.08 / 12} &=\$ 5000 \\[4pt] \mathrm{m}(40.5356) &=\$ 5000 \\[4pt] \mathrm{m} &=\frac{5000}{40.5356}\\[4pt] &=\$ 123.35 \end{align*}\]
Robert needs to deposit $123.35 at the end of each month for 3 years into an account paying 8% compounded monthly in order to have $5,000 at the end of 5 years.
Example \(\PageIndex{4}\)
Suppose you contribute $500 each month into an ordinary annuity earning 6.25% compounded monthly. How long do you need to continue making contributions so that you will have at least $1,000,000?
Solution
Contributing $500 each month, \(m=500\). Interest is 6.25% compounded monthly, so \(r=0.0625\) and \(n=12\). You want a future value of $1,000,000 so \(A=1,000,000\).
\(1,000,000=\frac{500\left[(\mathbf{1}+0.0625 / 12)^{12 \mathbf{t}}-\mathbf{1}\right]}{0.0625 / 12} \)
Multiply both sides by \((0.0625 / 12) \) to clear the denominator:
\(1,000,000 \cdot (0.0625 / 12) = 500\left[(\mathbf{1}+0.0625 / 12)^{12 \mathbf{t}}-\mathbf{1}\right] \)
Divide both sides by 500:
\(\dfrac{1,000,000 \cdot (0.0625 / 12)}{500} = (\mathbf{1}+0.0625 / 12)^{12 \mathbf{t}}-\mathbf{1} \)
Add 1 to both sides:
\(\dfrac{1,000,000 \cdot (0.0625 / 12)}{500}+1 = (\mathbf{1}+0.0625 / 12)^{12 \mathbf{t}}\)
Convert to logarithmic form to isolate the exponent:
\( \log_{1+0.0625/12}(\dfrac{1,000,000 \cdot (0.0625 / 12)}{500}+1) = 12 \mathbf{t}\)
Use change of base formula:
\( \dfrac{\log(\dfrac{1,000,000 \cdot (0.0625 / 12)}{500}+1)}{\log(1+0.0625/12)} = 12 \mathbf{t}\)
Enter into calculator:
\(468.75=t\)
Divide both sides by 12:
\( 39.06=t\)
It will take approximately 39 years for you to have at least $1,000,000.
Sinking Fund
When a business deposits money at regular intervals into an account in order to save for a future purchase of equipment, the savings fund is referred to as a “ sinking fund ”. Calculating the sinking fund deposit uses the same method as the previous problem.
Example \(\PageIndex{5}\)
A business needs $450,000 in five years. How much should be deposited each quarter in a sinking fund that earns 9% compounded quarterly to have this amount in five years?
Solution
Again, suppose that \(m\) dollars are deposited each quarter in the sinking fund. After five years, the future value of the fund should be $450,000. This suggests the following relationship:
\[\begin{align*} \dfrac{\mathrm{m}\left[(1+ 0.09 / 4)^{20}-1\right]}{0.09 / 4} &=\$ 450,000 \\[4pt] \mathrm{m}(24.9115) &=450,000 \\[4pt]
\mathrm{m} &=\dfrac{450000}{24.9115} \\[4pt] &=\$ 18,063.93 \end{align*}\]
The business needs to deposit $18,063.93 at the end of each quarter for 5 years into an sinking fund earning interest of 9% compounded quarterly in order to have $450,000 at the end of 5 years.
Annuity Due
If the payment is made at the beginning of each period, rather than at the end, we call it an annuity due . The formula for the annuity due can be derived in a similar manner. Reconsider Example 1, with the change that the deposits are made at the beginning of each month.
Example \(\PageIndex{6}\)
If at the beginning of each month a deposit of $500 is made in an account that pays 8% compounded monthly, what will the final amount be after five years?
Solution
There are 60 deposits made in this account. The first payment stays in the account for 60 months, the second payment for 59 months, the third for 58 months, and so on.
- The first payment of $500 will accumulate to an amount of \($500(1 + 0.08/12)^{60}\).
- The second payment of $500 will accumulate to an amount of \($500(1 + .08/12)^{59}\).
- The third payment will accumulate to \($500(1 + 0.08/12)^{58}\).
And so on . . .
The last payment is in the account for a month and accumulates to \($500(1 + 0.08/12)\)
To find the total amount in five years, we need to find the sum of the series:
\[$500(1 + 0.08/12)^{60} + $500(1 + 0.08/12)^{59} + $500(1 + 0.08/12)^{58} + \ldots + $500(1 + 0.08/12) \nonumber\]
Written backwards, we have
\[$500(1 + 0.08/12) + $500(1 + 0.08/12)^2 + \ldots + $500(1 + 0.08/12)^{60} \nonumber\]
If we add $500 to this series, and later subtract that $500, the value will not change. We get
\[\textbf{\$500} + $500(1 + 0.08/12) + $500(1 + 0.08/12)^2 + \ldots + $500(1 + 0.08/12)^{60} - \textbf{\$500} \nonumber\]
Except for the last term, we have a geometric series with \(a\) = $500, \(r\) = (1 + .08/12), and \(n\) = 60. Therefore the sum is
\[\begin{align*} \mathrm{A} &=\frac{\$ 500\left[(1+0.08 / 12)^{61}-1\right]}{0.08 / 12}-\$ 500 \\[4pt] &=\$ 500(74.9667)-\$ 500 \\[4pt] &=\$ 37483.35-\$ 500 \\[4pt] &=\$ 36983.35 \end{align*}\]
So, in the case of an annuity due, to find the future value, we increase the number of periods \(n\) by 1, and subtract one payment.
Future Value of an "Annuity Due"
\[\mathrm{A}=\frac{\mathrm{m}\left[(1+\mathrm{r} / \mathrm{n})^{\mathrm{nt}+1}-1\right]}{\mathrm{r} / \mathrm{n}}-\mathrm{m} \nonumber\]
Most of the problems we are going to do in this chapter involve ordinary annuities, therefore, we will down play the significance of the last formula for the annuity due. We mentioned the formula for the annuity due only for completeness.
Summary
Finally, it is the author's wish that the student learn the concepts in a way that he or she will not have to memorize every formula. It is for this reason formulas are kept at a minimum. But before we conclude this section we will once again mention one single equation that will help us find the future value, as well as the sinking fund payment.
If a payment of \(m\) dollars is made in an account \(n\) times a year at an interest \(r\), then the future value \(\mathrm{A}\) after \(t\) years is
\[\mathbf{A}=\frac{\mathbf{m}\left[(\mathbf{1}+\mathbf{r} / \mathbf{n})^{\mathbf{n t}}-\mathbf{1} \right]}{\mathbf{r} / \mathbf{n}} \nonumber\]
Note that the formula assumes that the payment period is the same as the compounding period. If these are not the same, then this formula does not apply.


Key Terms
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coordinate
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A number paired with a point on a number line.
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counting numbers
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The counting numbers are the numbers 1, 2, 3, ….
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difference
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The result of subtracting two or more numbers.
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dividend
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The number being divided when dividing two numbers.
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divisor
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The number dividing the dividend when dividing two numbers.
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number line
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A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.
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origin
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The point labeled 0 on a number line.
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place value system
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Our number system is called a place value system because the value of a digit depends on its position, or place, in a number.
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product
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The result of multiplying two or more numbers.
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quotient
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The result of dividing two numbers.
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rounding
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The process of approximating a number.
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sum
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The result of adding two or more numbers.
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whole numbers
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The whole numbers are the numbers 0, 1, 2, 3, ….
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Key Concepts
1.1 - Introduction to Whole Numbers
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Name a whole number in words.
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Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones.
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Use commas in the number to separate the periods.
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Use place value to write a whole number.
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Identify the words that indicate periods. (Remember the ones period is never named.)
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Draw three blanks to indicate the number of places needed in each period.
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Name the number in each period and place the digits in the correct place value position.
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Round a whole number to a specific place value.
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Locate the given place value. All digits to the left of that place value do not change.
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Underline the digit to the right of the given place value.
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Determine if this digit is greater than or equal to 5. If yes—add 1 to the digit in the given place value. If no—do not change the digit in the given place value.
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Replace all digits to the right of the given place value with zeros.
1.2 - Add Whole Numbers
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Addition Notation:
To describe addition, we can use symbols and words.
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Operation
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Notation
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Expression
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Read as
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Result
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Addition
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+
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3 + 4
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three plus four
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the sum of 3 and 4
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Identity Property of Addition:
The sum of any number a and 0 is the number. $$\begin{split} a + 0 &= a \\ 0 + a &= a \end{split}$$
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Commutative Property of Addition:
Changing the order of the addends a and b does not change their sum. $$a + b = b + a \ldotp$$
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Add whole numbers
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Write the numbers so each place value lines up vertically.
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Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than 9, carry to the next place value.
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Continue adding each place value from right to left, adding each place value and carrying if needed.
1.3 - Subtract Whole Numbers
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Operation
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Notation
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Expression
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Read as
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Result
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Subtraction
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7 |
seven minus three
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the difference of 7 and 3
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Write the numbers so each place value lines up vertically.
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Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
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Continue subtracting each place value from right to left, borrowing if needed.
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Check by adding.
1.4 - Multiply Whole Numbers
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Operation
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Notation
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Expression
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Read as
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Result
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Multiplication
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×
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3 × 8
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three times eight
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the product of 3 and 8
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•
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3 • 8
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()
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3(8)
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Multiplication Property of Zero:
The product of any number and 0 is 0. $$\begin{split}a \cdot 0 &= 0 \\ 0 \cdot a &= 0 \end{split}$$
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Identity Property of Multiplication:
The product of any number and 1 is the number. $$\begin{split} 1 \cdot a &= a \\ a \cdot 1 &= a \end{split}$$
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Commutative Property of Multiplication:
Changing the order of the factors does not change their product. $$a \cdot b = b \cdot a \ldotp$$
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Multiply two whole numbers to find the product
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Write the numbers so each place value lines up vertically.
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Multiply the digits in each place value.
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Work from right to left, starting with the ones place in the bottom number.
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Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
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If a product in a place value is more than 9, carry to the next place value.
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Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
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Insert a zero as a placeholder with each additional partial product.
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Add the partial products.
1.5 - Divide Whole Numbers
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Operation
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Notation
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Expression
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Read as
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Result
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Division
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÷
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12 ÷ 4
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Twelve divided by four
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the quotient of 12 and 4
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\(\dfrac{a}{b}\)
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\(\dfrac{12}{4}\)
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\(b \overline{) a}\)
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\(4 \overline{\smash{)}12}\)
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a / b
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12 / 4
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Division Properties of One:
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Any number (except 0) divided by itself is one. $$a \div a = 1$$
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Any number divided by one is the same number. $$a \div 1 = a$$
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Division Properties of Zero:
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Zero divided by any number is 0. $$0 \div a = 0 $$
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Dividing a number by zero is undefined. $$a \div 0 = undefined$$
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Divide whole numbers
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Divide the first digit of the dividend by the divisor. If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.
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Write the quotient above the dividend.
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Multiply the quotient by the divisor and write the product under the dividend.
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Subtract that product from the dividend.
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Bring down the next digit of the dividend.
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Repeat from Step 1 until there are no more digits in the dividend to bring down.
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Check by multiplying the quotient times the divisor.
Contributors and Attributions


11.6: Reading- Penetration Pricing
What Is Penetration Pricing?
Penetration pricing is a pricing strategy in which the price of a product is initially set low to rapidly reach a wide fraction of the market and initiate word of mouth. [1] The strategy works on the assumption that customers will switch to the new product because of the lower price. Penetration pricing is most commonly associated with marketing objectives of enlarging market share and exploiting economies of scale or experience.
Returning to our economic model, below, you can see that penetration pricing focuses at the bottom of the demand curve. If the initial price is set low, at $2, for instance, the quantity demanded will be high: 400 units.
Penetration pricing offers a lower price in order to draw in a higher demand from consumers.
Why Might Penetration Pricing Make Sense?
Like skim pricing, penetration pricing shows an awareness of the dynamics in the product life cycle. The advantages of penetration pricing to the firm are the following:
- It can result in fast diffusion and adoption across the product life cycle. The strategy can achieve high market penetration rates quickly, taking competitors by surprise and not giving them time to react.
- It can create goodwill among the Innovators and Early Adopters, which can generate more demand via word of mouth.
- It establishes cost-control and cost-reduction pressures from the start, leading to greater efficiency.
- It discourages the entry of competitors.
- It can generate high stock turnover throughout the distribution channel, which creates important enthusiasm and support in the channel.
The main disadvantage of penetration pricing is that it establishes long-term price expectations for the product and image preconceptions for the brand and company. Both can make it difficult to raise prices later. Another potential disadvantage is that the low profit margins may not be sustainable long enough for the strategy to be effective.
- J Dean (1976). "Pricing Policies for New Products." Harvard Business Review 54 (6): 141–153. ↵
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- Penetration Pricing. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Penetration_pricing#cite_note-4 . License : CC BY-SA: Attribution-ShareAlike
- Mallards Feeding. Authored by : Yankech Gary. Located at : https://www.flickr.com/photos/49663413@N08/6965646827/ . License : CC BY-ND: Attribution-NoDerivatives


7.2A: Alternative to Glycolysis- the Entner-Doudoroff Pathway
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- Boundless
- Boundless
Learning Objectives
- Distinguish between the Entner-Doudoroff pathway and glycolysis
The Entner–Doudoroff pathway describes an alternate series of reactions that catabolize glucose to pyruvate using a set of enzymes different from those used in either glycolysis or the pentose phosphate pathway. Glycolysis (from glycose, an older term for glucose + -lysis degradation) is the metabolic pathway that converts glucose \(\ce{C6H12O6}\), into pyruvate, \(\ce{CH3COCOO^{−} }\). The free energy released in this process is used to form the high-energy compounds ATP (adenosine triphosphate) and NADH (reduced nicotinamide adenine dinucleotide). Most bacteria use glycolysis and the pentose phosphate pathway. This pathway was first reported in 1952 by Michael Doudoroff and Nathan Entner.
Distinct features of the Entner–Doudoroff pathway are that it occurs only in prokaryotes and it uses 6-phosphogluconate dehydratase and 2-keto-3-deoxyphosphogluconate aldolase to create pyruvate from glucose. The Entner–Doudoroff pathway has a net yield of 1 ATP for every glucose molecule processed, as well as 1 NADH and 1 NADPH. By comparison, glycolysis has a net yield of 2 ATP and 2 NADH for every one glucose molecule processed.
There are a few bacteria that substitute classic glycolysis with the Entner-Doudoroff pathway. They may lack enzymes essential for glycolysis, such as phosphofructokinase-1. This pathway is generally found in Pseudomonas , Rhizobium , Azotobacter , Agrobacterium , and a few other Gram-negative genera. Very few Gram-positive bacteria have this pathway, with Enterococcus faecalis being a rare exception. Most organisms that use the pathway are aerobes due to the low ATP yield per glucose such as Pseudomonas, a genus of Gram-negative bacteria, and Azotobacter, a genus of Gram-negative bacteria.
Key Points
- Glycolysis is the metabolic pathway that converts glucose into pyruvate and hydrogen ions.
- The Entner-Doudoroff pathway was first reported in 1952 by Michael Doudoroff and Nathan Entner.
- There are a few bacteria that substitute classic glycolysis with the Entner-Doudoroff pathway.
Key Terms
- glycolysis : The metabolic pathway that converts glucose into pyruvate and hydrogen ions.
- ATP : Adenosine-5′-triphosphate (ATP) is a multifunctional nucleoside triphosphate used in cells as a coenzyme. It is often called the “molecular unit of currency” of intracellular energy transfer. ATP transports chemical energy within cells for metabolism.


2.7: Conditionals
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So far, we have learned how to translate and construct truth tables for three truth-functional connectives. However, there is one more truth functional connective that we have not yet learned: the conditional. 2 The English phrase that is most often used to express conditional statements is “if...then.” For example,
If it is raining then the ground it wet.
Like conjunctions and disjunctions, conditionals connect two atomic propositions. There are two atomic propositions in the above conditional:
It is raining.
The ground it wet.
The proposition that follows the “if” is called the antecedent of the conditional and the proposition that follows the “then” is call the consequent of the conditional. The conditional statement above is not asserting either of these atomic propositions. Rather, it is telling us about the relationship between them. Let’s symbolize “it is raining” as “R” and “the ground is wet” as “G.” Thus, our symbolization of the above conditional would be:
R ⊃ G
The “⊃” symbol is called the “horseshoe” and it represents what is called the “material conditional.” A material conditional is defined as being true in every case except when the antecedent is true and the consequent is false. Below is the truth table for the material conditional. Notice that, as just stated, there is only one scenario in which we count the conditional false: when the antecedent is true and the consequent false.
| p | q | p ⊃ q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Let’s see how this applies to the above conditional, “if it is raining, then the ground is wet.” As before, we can think about the meaning of the truth functional connectives by asking whether the sentences containing those connectives would be true or false in the four possible scenarios. The first two are pretty easy. If I assert the above conditional “if it is raining then the ground is wet” when it is both raining and the ground is wet (i.e., the first line of the truth table below), then the conditional statement would be true in that scenario. However, if I assert it and it is raining but the ground isn’t wet (i.e., the second line of the truth table below), then my statement has been shown to be false. Why? Because I’m asserting that any time it is raining, the ground is wet. But if it is raining but the ground isn’t wet, then this scenario is a counterexample to my claim—it shows that my claim is false. Now consider the scenario in which it is not raining but the ground is wet. Would this scenario show that my conditional statement is false? No, it wouldn’t. The reason is that the conditional statement R ⊃ G is only asserting something about what is the case when it is raining. So this conditional statement isn’t asserting anything about those scenarios in which it isn’t raining. I’m only saying that when it is raining, the ground is wet. But that doesn’t mean that the ground couldn’t be wet for other reasons (e.g., a sprinkler watering the grass). So the meaning of the material conditional should count a statement true whenever its antecedent is false. Thus, in a scenario in which it is neither raining nor the ground is wet (i.e., the fourth line of the truth table), the conditional statement should still be true. Would the fact of a sunny day and dry ground show that the conditional R ⊃ G is false? Of course not! Thus, as we’ve seen, the material conditional is false only when the antecedent is true and the consequent is false.
| R | G | R ⊃ G |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
It is sometimes helpful to think of the material conditional as a rule. For example, suppose that I tell my class:
If you pass all the exams, you will pass the course.
Let’s symbolize “you pass all the exams” as “E” and “you pass the course” as “C.” We would then symbolize the conditional as:
E ⊃ C
Under what conditions would my statement E ⊃ C be shown to be false? There are four possible scenarios:
| E | C | E ⊃ C |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Suppose that you pass all the exams and pass the class (first row). That would confirm my conditional statement E ⊃ C. Suppose, on the other hand, that although you passed all the exams, you did not pass the class (second row). This would should my statement is false (and you would have legitimate grounds for complaint!).  My statement allows this to be true and it is important to see why. When I assert E ⊃ C I am not asserting anything about the situation in
which E is false. I am simply saying that one way of passing the course is by passing all of the exams; but that doesn’t mean there aren’t other ways of passing the course. Finally, consider the case in which you do not pass all the exams and you also do not pass the course (fourth row). For the same reason, this scenario is compatible with my statement being true. Thus, again, we see that a material conditional is false in only one circumstance: when the antecedent is true and the consequent is false.
There are other English phrases that are commonly used to express conditional statements. Here are some equivalent ways of expressing the conditional, “if it is raining then the ground is wet”:
It is raining only if the ground is wet
The ground is wet if is raining
Only if the ground is wet is it raining
That it is raining implies that the ground is wet
That it is raining entails that the ground is wet
As long as it is raining, the ground will be wet
So long as it is raining, the ground will be wet
The ground is wet, provided that it is raining
Whenever it is raining, the ground is wet
If it is raining, the ground is wet
All of these conditional statements are symbolized the same way, namely R ⊃ G. The antecedent of a conditional statement always lays down what logicians call a sufficient condition. A sufficient condition is a condition that suffices for some other condition to obtain. To say that x is a sufficient condition for y is to say that any time x is present, y will thereby be present. For example, a sufficient condition for dying is being decapitated; a sufficient condition for being a U.S. citizen is being born in the U.S. The consequent of a conditional statement always lays down a necessary condition. A necessary condition is a condition that must be in present in order for some other condition to obtain. To say that x is a necessary condition for y is to say that if x were not present, y would not be present either. For example, a necessary condition for being President of the U.S. is being a U.S. citizen; a necessary condition for having a brother is having a sibling. Notice, however, that being a U.S. citizen is not a sufficient condition for being President, and having a sibling is not a sufficient condition for having a brother. Likewise, being born in the U.S. is not a necessary condition for being a U.S. citizen (people can become “naturalized citizens”), and being decapitated is not a necessary condition for dying (one can die without being decapitated).
Exercise
Translate the following English sentences into symbolic logic sentences using the constants indicated. Make sure you write out what the atomic propositions are. In some cases this will be straightforward, but not in every case. Remember: atomic propositions never contain any truth functional connectives—and that includes negation! Note: although many of these sentences can be translated using only the horseshoe, others require truth functional connectives other than the horseshoe.
1. The Tigers will win only if the Indians lose their star pitcher. (T, I)
2. Tom will pass the class provided that he does all the homework. (P, H)
3. The car will run only if it has gas. (R, G)
4. The fact that you are asking me about your grade implies that you care about your grade. (A, C)
5. Although Frog will swim without a bathing suit, Toad will swim only if he is wearing a bathing suit. (F, T, B)
6. If Obama isn’t a U.S. citizen, then I’m a monkey’s uncle. (O, M)
7. If Toad wears his bathing suit, he doesn’t want Frog to see him in it. (T, F)
8.  (P, S, L)
9. Bekele will win the race as long as he stays healthy. (W, H)
10. If Bekele is either sick or injured, he will not win the race. (S, I, W)
11.  (P, C, S)
12. If that plant has three leaves then it is poisonous. (T, P)
13. The fact that the plant is poisonous implies that it has three leaves. (T, P)
14. The plant is poisonous only if it has three leaves. (T, P)
15. The plant has three leaves if it is poisonous. (T, P)
16. Olga will swim in the open water as long as there is a shark net present. (O, N)
17. Olga will swim in the open water only if there is shark net. (O, N)
18. The fact that Olga is swimming implies that she is wearing a bathing suit. (O, B)
19. If Olga is in Nice, she does not wear a bathing suit. (N, B)
20. If Terrence pulls Philip’s finger, something bad will happen. (T, B)
2 Actually, there is one more truth functional connective that we will not be learning and that is what is called the “biconditional” or “material equivalence.” However, since the biconditional is equivalent to a conjunction of two different conditionals, we don’t actually need it. Although I will discuss material equivalence in section 2.9, we will not be regularly using it.