5.3: Compound Statements
Learning Objectives
After completing this section, you should be able to:
- Translate compound statements into symbolic form.
- Translate compound statements in symbolic form with parentheses into words.
- Apply the dominance of connectives.
Suppose your friend is trying to get a license to drive. In most places, they will need to pass some form of written test proving their knowledge of the laws and rules for driving safely. After passing the written test, your friend must also pass a road test to demonstrate that they can perform the physical task of driving safely within the rules of the law.
Consider the statement: "My friend passed the written test, but they did not pass the road test." This is an example of a compound statement , a statement formed by using a connective to join two independent clauses or logical statements. The statement, “My friend passed the written test,” is an independent clause because it is a complete thought or idea that can stand on its own. The second independent clause in this compound statement is, “My friend did not pass the road test.” The word "but" is the connective used to join these two statements together, forming a compound statement. So, did your friend acquire their driving license?.
This section introduces common logical connectives and their symbols, and allows you to practice translating compound statements between words and symbols. It also explores the order of operations, or dominance of connectives, when a single compound statement uses multiple connectives.
Common Logical Connectives
Understanding the following logical connectives, along with their properties, symbols, and names, will be key to applying the topics presented in this chapter. The chapter will discuss each connective introduced here in more detail.
The joining of two logical statements with the word "and" or "but" forms a compound statement called a conjunction . In logic, for a conjunction to be true, all the independent logical statements that make it up must be true. The symbol for a conjunction is . Consider the compound statement, “Derek Jeter played professional baseball for the New York Yankees, and he was a shortstop.” If represents the statement, “Derrick Jeter played professional baseball for the New York Yankees,” and if represents the statement, “Derrick Jeter was a short stop,” then the conjunction will be written symbolically as
The joining of two logical statements with the word “or” forms a compound statement called a disjunction . Unless otherwise specified, a disjunction is an inclusive or statement, which means the compound statement formed by joining two independent clauses with the word or will be true if a least one of the clauses is true. Consider the compound statement, "The office manager ordered cake for for an employee’s birthday or they ordered ice cream.” This is a disjunction because it combines the independent clause, “The office manager ordered cake for an employee’s birthday,” with the independent clause, “The office manager ordered ice cream,” using the connective, or . This disjunction is true if the office manager ordered only cake, only ice cream, or they ordered both cake and ice cream. Inclusive or means you can have one, or the other, or both!
Joining two logical statements with the word implies , or using the phrase “if first statement , then second statement,” is called a conditional or implication . The clause associated with the "if" statement is also called the hypothesis or antecedent , while the clause following the "then" statement or the word implies is called the conclusion or consequent . The conditional statement is like a one-way contract or promise. The only time the conditional statement is false, is if the hypothesis is true and the conclusion is false. Consider the following conditional statement, “If Pedro does his homework, then he can play video games.” The hypothesis/antecedent is the statement following the word if , which is “Pedro does/did his homework.” The conclusion/consequent is the statement following the word then , which is “Pedro can play his video games.”
Joining two logical statements with the connective phrase “if and only if” is called a biconditional . The connective phrase "if and only if" is represented by the symbol, In the biconditional statement, is called the hypothesis or antecedent and is called the conclusion or consequent. For a biconditional statement to be true, the truth values of and must match. They must both be true, or both be false.
The table below lists the most common connectives used in logic, along with their symbolic forms, and the common names used to describe each connective.
Table \(\PageIndex{1}\)
| Connective | Symbol | Name |
|---|---|---|
|
and
but |
conjunction | |
| or | disjunction, inclusive or | |
| not | ~ | negation |
| if , then implies | conditional, implication | |
| if and only if | biconditional |
Checkpoint
These connectives, along with their names, symbols, and properties, will be used throughout this chapter and should be memorized.
Associate Connectives with Symbols and Names
For each of the following connectives, write its name and associated symbol.
- or
- implies
- but
Solution
- A compound statement formed with the connective word or is called a disjunction, and it is represented by the symbol.
- A compound statement formed with the connective word implies or phrase “ if …, then” is called a conditional statement or implication and is represented by the symbol.
- A compound statement formed with the connective words but or and is called a conjunction, and it is represented by the symbol.
For each connective write its name and associated symbol.
- not
- and
- if and only if
Translating Compound Statements to Symbolic Form
To translate a compound statement into symbolic form, we take the following steps.
- Identify and label all independent affirmative logical statements with a lower case letter, such as , , or .
- Identify and label any negative logical statements with a lowercase letter preceded by the negation symbol, such as , , or .
- Replace the connective words with the symbols that represent them, such as
Consider the previous example of your friend trying to get their driver’s license. Your friend passed the written test, but they did not pass the road test. Let represent the statement, “My friend passed the written test.” And, let represent the statement, “My friend did not pass the road test.” Because the connective but is logically equivalent to the word and , the symbol for but is the same as the symbol for and ; replace but with the symbol The compound statement is symbolically written as: . My friend passed the written test, but they did not pass the road test.
Checkpoint
When translating English statements into symbolic form, do not assume that every connective “and” means you are dealing with a compound statement. The statement, “The stripes on the U.S. flag are red and white,” is a simple statement. The word “white” doesn’t express a complete thought, so it is not an independent clause and does not get its own symbol. This statement should be represented by a single letter, such as : The stripes on the U.S. flag are red and white.
Translating Compound Statements into Symbolic Form
Let represent the statement, “It is a warm sunny day,” and let represent the statement, “the family will go to the beach.” Write the symbolic form of each of the following compound statements.
- If it is a warm sunny day, then the family will go to the beach.
- The family will go to the beach, and it is a warm sunny day.
- The family will not go to the beach if and only if it is not a warm sunny day.
- The family not go to the beach, or it is a warm sunny day.
- Answer
-
- Replace “it is a warm sunny day” with . Replace “the family will go to the beach.” with . Next. Next, because the connective is if …, then place the conditional symbol, , between and . The compound statement is written symbolically as:
- Replace “The family will go to the beach” with . Replace “it is a warm sunny day.” with . Next, because the connective is and , place the symbol between and . The compound statement is written symbolically as:
- Replace “The family will not go to the beach. with . Replace “it is not a warm sunny day” with . Next, because the connective is or , if and only if , place the biconditional symbol, between and . The compound statement is written symbolically as:
- Replace “The family will not go to the beach” with . Replace “it is a warm sunny day” with . Next, because the connective is or , place the symbol between and . The compound statement is written symbolically as:
Let p represent the statement, “Last night it snowed,” and let q represent the statement, “Today we will go skiing.” Write the symbolic form of each of the following compound statements:
- Today we will go skiing, but last night it did not snow.
- Today we will go skiing if and only if it snowed last night.
- Last night is snowed or today we will not go skiing.
- If it snowed last night, then today we will go skiing.
Translating Compound Statements in Symbolic Form with Parentheses into Words
When parentheses are written in a logical argument, they group a compound statement together just like when calculating numerical or algebraic expressions. Any statement in parentheses should be treated as a single component of the expression. If multiple parentheses are present, work with the inner most parentheses first.
Consider your friend’s struggles to get their license to drive. Let represent the statement, “My friend passed the written test,” let represent the statement, “My friend passed the road test,” and let represent the statement, “My friend received a driver’s license.” The statement can be translated into words as follows: the statement is grouped together to form the hypothesis of the conditional statement and is the conclusion. The conditional statement has the form “ if then ” Therefore, the written form of this statement is: “If my friend passed the written test and they passed the road test, then my friend received a driver’s license.”
Sometimes a compound statement within parentheses may need to be negated as a group. To accomplish this, add the phrase, “it is not the case that” before the translation of the phrase in parentheses. For example, using , , and of your friend obtaining a license, let’s translate the statement into words.
In this case, the hypothesis of the conditional statement is and the conclusion is To negate the hypothesis, add the phrase “it is not the case” before translating what is in parentheses. The translation of the hypothesis is the sentence, “It is not the case that my friend passed the written test and they passed the road test,” and the translation of the conclusion is, “My friend did not receive a driver’s license.” So, a translation of the complete conditional statement, is: “If it is not the case that my friend passed the written test and the road test, then my friend did not receive a driver’s license.”
Checkpoint
It is acceptable to interchange proper names with pronouns and remove repeated phrases to make the written statement more readable, as long the meaning of the logical statement is not changed.
Video
Translating Compound Statements in Symbolic Form with Parentheses into Words
Let represent the statement, “My child finished their homework,” let represent the statement, “My child cleaned her room,” let represent the statement, “My child played video games,” and let represent the statement, “My child streamed a movie.” Translate each of the following symbolic statements into words.
- Answer
-
- Replace ~ with “It is not the case,” and with “and.” One possible translation is: “It is not the case that my child finished their homework and cleaned their room.”
- The hypothesis of the conditional statement is, “My child finished their homework and cleaned their room.” The conclusion of the conditional statement is, “My child played video games or streamed a movie.” One possible translation of the entire statement is: “If my child finished their homework and cleaned their room, then they played video games or streamed a movie.”
- The hypothesis of the biconditional statement is and is written in words as: “It is not the case that my child played video games or streamed a movie.” The conclusion of the biconditional statement is , which translates to: “It is not the case that my child finished their homework and cleaned their room.” Because the biconditional, translates to if and only if , one possible translation of the statement is: “It is not the case that my child played video games or streamed a movie if and only if it is not the case that my child finished their homework and cleaned their room.”
Let p represent the statement, “My roommates ordered pizza,” let q represent the statement, “I ordered wings,” and let r be the statement, “Our friends came over to watch the game.” Translate the following statements into words.
1. ~r→(p∨q)
2. /**/\text{~}(p \vee r)/**/
The Dominance of Connectives
The order of operations for working with algebraic and arithmetic expressions provides a set of rules that allow consistent results. For example, if you were presented with the problem , and you were not familiar with the order of operation, you might assume that you calculate the problem from left to right. If you did so, you would add 1 and 3 to get 4, and then multiply this answer by 2 to get 8, resulting in an incorrect answer. Try inputting this expression into a scientific calculator. If you do, the calculator should return a value of 7, not 8.
The order of operations for algebraic and arithmetic operations states that all multiplication must be applied prior to any addition. Parentheses are used to indicate which operation—addition or multiplication—should be done first. Adding parentheses can change and/or clarify the order. The parentheses in the expression indicate that 3 should be multiplied by 2 to get 6, and then 1 should be added to 6 to get 7:
As with algebraic expressions, there is a set of rules that must be applied to compound logical statements in order to evaluate them with consistent results. This set of rules is called the dominance of connectives . When evaluating compound logical statements, connectives are evaluated from least dominant to most dominant as follows:
- Parentheses are the least dominant connective. So, any expression inside parentheses must be evaluated first. Add as many parentheses as needed to any statement to specify the order to evaluate each connective.
- Next, we evaluate negations.
- Then, we evaluate conjunctions and disjunctions from left to right, because they have equal dominance.
- After evaluating all conjunctions and disjunctions, we evaluate conditionals.
- Lastly, we evaluate the most dominant connective, the biconditional. If a statement includes multiple connectives of equal dominance, then we will evaluate them from left to right.
See Figure 2.7 for a visual breakdown of the dominance of connectives.
Let’s revisit your friend’s struggles to get their driver’s license. Let represent the statement, “My friend passed the written test,” let represent the statement, “My friend passed the road test,” and let represent the statement, “My friend received a driver’s license.” Let's use the dominance of connectives to determine how the compound statement should be evaluated.
Step 1: There are no parentheses, which is least dominant of all connectives, so we can skip over that.
Step 2: Because negation is the next least dominant, we should evaluate first. We could add parentheses to the statement to make it clearer which connecting needs to be evaluated first: is equivalent to
Step 3: Next, we evaluate the conjunction, . is equivalent to
Step 4: Finally, we evaluate the conditional, as this is the most dominant connective in this compound statement.
Who Knew?
When using spreadsheet applications, like Microsoft Excel or Google Sheets, have you noticed that core functions, such as sum, average, or rate, have the same name and syntax for use? This is not a coincidence. Various standards organizations have developed requirements that software developers must implement to meet the conditions set by governments and large customers worldwide. The OpenDocument Format OASIS Standard enables transferring data between different office productivity applications and was approved by the International Standards Organization (ISO) and IEC on May 6, 2006.
Prior to adopting these standards, a government entity, business, or individual could lose access to their own data simply because it was saved in a format no longer supported by a proprietary software product—even data they were required by law to preserve, or data they simply wished to maintain access to.
Just as rules for applying the dominance of connectives help maintain understanding and consistency when writing and interpreting compound logical statements and arguments, the standards adopted for database software maintain global integrity and accessibility across platforms and user bases.
Applying the Dominance of Connectives
For each of the following compound logical statements, add parentheses to indicate the order to evaluate the statement. Recall that parentheses are evaluated innermost first.
- Answer
-
- Because negation is the least dominant connective, we evaluate it first: Because conjunction and disjunction have the same dominance, we evaluate them left to right. So, we evaluate the conjunction next, as indicated by the additional set of parentheses: The only remaining connective is the disjunction, so it is evaluated last, as indicated by the third set of parentheses. The complete solution is:
- Negation has the lowest dominance, so it is evaluated first: The remaining connectives are the conditional and the conjunction. Because conjunction has a lower precedence than the conditional, it is evaluated next, as indicated by the second set of parentheses: The last step is to evaluate the conditional, as indicated by the third set of parentheses:
-
This statement is known as De Morgan’s Law for the negation of a disjunction. It is always true. Section 2.6 of this chapter will explore De Morgan’s Laws in more detail.
- First, we evaluate the negations on the right side of the biconditional prior to the conjunction.
- Then, we evaluate the disjunction on the left side of the biconditional, followed by the negation of the disjunction on the left side.
- Lastly, after completely evaluating each side of the biconditional, we evaluate the biconditional. It does not matter which side you begin with.
1. \(p \vee q \wedge \sim r\)
2. \(\sim p \rightarrow q \vee r\)
3. \(\sim p \vee \sim q \leftrightarrow \sim(p \wedge q)\)
WORK IT OUT
Logic Terms and Properties – Matching Game
Materials: For every group of four students, include 30 cards (game, trading, or playing cards), 30 individual clear plastic gaming card sleeves, and 30 card-size pieces of paper. Prepare a list of 60 questions and answers ahead of time related to definitions and problems in Statements and Quantifiers and Compound Statements. Provide each group of four students with 20 questions and their associated answers. Instruct each group to select 15 of the 20 questions, and then, for each problem selected, create one card with the question and one card with the answer. Instruct the groups to then place each problem and answer in a separate card sleeve. Once they create 15 problem cards and 15 answer cards, have students shuffle the set of cards.
To play the game, groups should exchange their card decks to ensure no team begins playing with the deck that they created. Split each four-person group into teams of two students. After shuffling the cards, one team lays cards face down on their desk in a five-by-six grid. The other team will go first.
Each player will have a turn to try matching the question with the correct answer by flipping two cards to the face up position. If a team makes a match, they get to flip another two cards; if they do not get a match, they flip the cards face down and it is the other team’s turn to flip over two cards. The game continues in this manner until teams match all question cards with their corresponding answer cards. The team with the most set of matching cards wins.
In the first module of this chapter, we evaluated the truth value of negations. In the following modules, we will discuss how to evaluate conjunctions, disjunctions, conditionals, and biconditionals, and then evaluate compound logical statements using truth tables and our knowledge of the dominance of connectives.
Check Your Understanding
1. A __________ __________ is a logical statement formed by combining two or more statements with connecting words, such as and, or, but, not, and if …, then.
2. A _____ is a word or symbol used to join two or more logical statements together to form a compound statement.
3. The most dominant connective is the _____.
4._____ are used to specify which logical connective should be evaluated first when evaluating a compound statement.
5. Both _____ and _____ have equal dominance and are evaluated from left to right when no parentheses are present in a compound logical statement.
Section 2.2 Exercises
For the following exercises, translate each compound statement into symbolic form.
For the following exercises, translate each compound statement into symbolic form.
Given \(p\) : "Layla has two weeks for vacation," \(q\) : "Marcus is Layla's friend," \(r\) : "Layla will travel to Paris, France," and \(s\) : "Layla and Marcus will travel together to Niagara Falls, Ontario."
1. If Layla has two weeks for vacation, then she will travel to Paris, France.
2. Layla and Marcus will travel together to Niagara Falls, Ontario or Layla will travel to Paris, France.
3. If Marcus is not Layla's friend, then they will not travel to Niagara Falls, Ontario together."
4. Layla and Marcus will travel to Niagara Falls, Ontario together if and only if Layla and Marcus are friends.
5. If Layla does not have two weeks for vacation and Marcus is Layla's friend, then Marcus and Layla will travel together to Niagara Falls, Ontario.
6. If Layla has two weeks for vacation and Marcus is not her friend, then she will travel to Paris, France.
For the following exercises, translate each compound statement into symbolic form.
Given \(p\) : "Tom is a cat," \(q\) : "Jerry is a mouse," \(r\) : "Spike is a dog," \(s\) : "Tom chases Jerry," and \(t\) : "Spike catches Tom."
7. Jerry is a mouse and Tom is a cat.
8. If Tom chases Jerry, then Spike will catch Tom.
9. If Spike does not catch Tom, then Tom did not chase Jerry.
10. Tom is a cat and Spike is a dog, or Jerry is not a Mouse.
11. It is not the case that Tom is not a cat and Jerry is not a mouse.
12. Spike is not a dog and Jerry is a mouse if and only if Tom chases Jerry, but Spike does not catch Tom.
For the following exercises, translate the symbolic form of each compound statement into words.
Given \(p\) : "Tracy Chapman plays guitar," \(q\) : "Joan Jett plays guitar," \(r\) : "All rock bands include guitarists," and \(s\) : "Elton John plays the piano."
13. \(p \vee r\)
14. \(\sim s \rightarrow \sim q\)
15. \((p \wedge q) \leftrightarrow r\)
16. \(\sim r \wedge(q \vee s)\)
17. \(\sim(p \wedge \sim q)\)
18. \((q \rightarrow \sim r) \leftrightarrow(\sim p \vee \sim r)\)
For the following exercises, translate the symbolic form of each compound statement into words.
Given \(p\) : "The median is the middle number," \(q\) : "The mode is the most frequent number," \(r\) : "The mean is the average number," \(s\) : "The median, mean, and mode are equal," and \(t\) : "The data set is symmetric."
19. \(t \rightarrow s\)
20. \(p \wedge(q \wedge r)\)
21. \(\sim t \rightarrow \sim s\)
22. \((r \wedge p) \leftrightarrow q\)
23. \((t \rightarrow \sim q) \vee(r \rightarrow s)\)
24. \(\sim(q \vee r) \rightarrow t\)
For the following exercises, apply the proper dominance of connectives by adding parentheses to indicate the order in which the statement must be evaluated.
25.


13.5: The Supreme Court
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Learning Objectives
By the end of this section, you will be able to:
- Analyze the structure and important features of the Supreme Court
- Explain how the Supreme Court selects cases to hear
- Discuss the Supreme Court’s processes and procedures
The Supreme Court of the United States, sometimes abbreviated SCOTUS, is a one-of-a-kind institution. While a look at the Supreme Court typically focuses on the nine justices themselves, they represent only the top layer of an entire branch of government that includes many administrators, lawyers, and assistants who contribute to and help run the overall judicial system. The Court has its own set of rules for choosing cases, and it follows a unique set of procedures for hearing them. Its decisions not only affect the outcome of the individual case before the justices, but they also create lasting impacts on legal and constitutional interpretation for the future.
The Structure of the Supreme Court
The original court in 1789 had six justices, but Congress set the number at nine in 1869, and it has remained there ever since. There is one chief justice, who is the lead or highest-ranking judge on the Court, and eight associate justices. All nine serve lifetime terms, after successful nomination by the president and confirmation by the Senate. There was discussion of expanding the court during Franklin D. Roosevelt's presidency and also during the 2020 presidential election. Nothing has come of court expansion, however.
The current court is fairly diverse in terms of gender, religion (Christians and Jews), ethnicity, and ideology, as well as length of tenure. Some justices have served for three decades, whereas others were only recently appointed by President Trump. Figure 13.9 lists the names of the nine justices serving on the Court as of June 2021 along with their year of appointment and the president who nominated them.
Currently, there are six justices who are considered part of the Court’s more conservative wing—Chief Justice Roberts and Associate Justices Thomas, Alito, Gorsuch, Kavanaugh, and Barrett—while three are considered more liberal-leaning—Justices Breyer, Sotomayor, and Kagan (Figure 13.10).
Link to Learning
While not formally connected with the public the way elected leaders are, the Supreme Court nonetheless offers visitors a great deal of information at its official website.
For unofficial summaries of recent Supreme Court cases or news about the Court, visit the Oyez website or SCOTUS blog.
In fact, none of the justices works completely in an ideological bubble. While their numerous opinions have revealed certain ideological tendencies, they still consider each case as it comes to them, and they don’t always rule in a consistently predictable or expected way. Furthermore, they don’t work exclusively on their own. Each justice has three or four law clerks, recent law school graduates who temporarily work for the justice, do research, help prepare the justice with background information, and assist with the writing of opinions. The law clerks’ work and recommendations influence whether the justices will choose to hear a case, as well as how they will rule. As the profile below reveals, the role of the clerks is as significant as it is varied.
Insider Perspective
Profile of a United States Supreme Court Clerk
A Supreme Court clerkship is one of the most sought-after legal positions, giving “thirty-six young lawyers each year a chance to leave their fingerprints all over constitutional law.” 47 A number of current and former justices were themselves clerks, including Chief Justice John Roberts, Justices Stephen Breyer and Elena Kagan, and former chief justice William Rehnquist.
Supreme Court clerks are often reluctant to share insider information about their experiences, but it is always fascinating and informative to hear about their jobs. Former clerk Philippa Scarlett, who worked for Justice Stephen Breyer, describes four main responsibilities: 48
Review the cases: Clerks participate in a “ cert. pool” (short for writ of certiorari , a request that the lower court send up its record of the case for review) and make recommendations about which cases the Court should choose to hear.
Prepare the justices for oral argument: Clerks analyze the filed briefs (short arguments explaining each party’s side of the case) and the law at issue in each case waiting to be heard.
Research and draft judicial opinions: Clerks do detailed research to assist justices in writing an opinion, whether it is the majority opinion or a dissenting or concurring opinion.
Help with emergencies: Clerks also assist the justices in deciding on emergency applications to the Court, many of which are applications by incarcerated people to stay their death sentences and are sometimes submitted within hours of a scheduled execution.
Explain the role of law clerks in the Supreme Court system. What is your opinion about the role they play and the justices’ reliance on them?
How the Supreme Court Selects Cases
Case names, written in italics, list the name of a petitioner versus a respondent, as in Roe v. Wade , for example. 50 For a case on appeal, you can tell which party lost at the lower level of court by looking at the case name: The party unhappy with the decision of the lower court is the one bringing the appeal and is thus the petitioner, or the first-named party in the case. For example, in Brown v. Board of Education (1954), Oliver Brown was one of the thirteen parents who brought suit against the Topeka public schools for discrimination based on racial segregation.
Most often, the petitioner is asking the Supreme Court to grant a writ of certiorari , a request that the lower court send up its record of the case for review. Once a writ of certiorari ( cert . for short) has been granted, the case is scheduled on the Court’s docket. The Supreme Court exercises discretion in the cases it chooses to hear, but four of the nine Justices must vote to accept a case. This is called the Rule of Four.
Past research indicated that the amount of interest-group activity surrounding a case before it is granted cert. has a significant impact on whether the Supreme Court puts the case on its agenda. The more activity, the more likely the case will be placed on the docket. 53 But more recent research broadens that perspective, suggesting that too much interest-group activity when the Court is considering a case for its docket may actually have diminishing impact and that external actors may have less influence on the work of the Court than they have had in the past. 54 Still, the Court takes into consideration external influences, not just from interest groups but also from the public, from media attention, and from a very key governmental actor—the solicitor general.
The solicitor general determines the position the government will take on a case. The attorneys of his or her office prepare and file the petitions and briefs, and the solicitor general (or an assistant) presents the oral arguments before the Court.
In other cases in which the United States is not the petitioner or the respondent, the solicitor general may choose to intervene or comment as a third party. Before a case is granted cert. , the justices will sometimes ask the solicitor general to comment on or file a brief in the case, indicating their potential interest in getting it on the docket. The solicitor general may also recommend that the justices decline to hear a case. Though research has shown that the solicitor general’s special influence on the Court is not unlimited, it remains quite significant. In particular, the Court does not always agree with the solicitor general, and “while justices are not lemmings who will unwittingly fall off legal cliffs for tortured solicitor general recommendations, they nevertheless often go along with them even when we least expect them to.” 56
Some have credited Donald B. Verrilli, the solicitor general under President Obama, with holding special sway over the five-justice majority ruling on same-sex marriage in June 2015. Indeed, his position that denying same-sex couples the right to marry would mean “thousands and thousands of people are going to live out their lives and go to their deaths without their states ever recognizing the equal dignity of their relationships” became a foundational point of the Court’s opinion, written by then-Justice Anthony Kennedy. 57 With such power over the Court, the solicitor general is sometimes referred to as “the tenth justice.”
Supreme Court Procedures
Once a case has been placed on the docket, briefs, or short arguments explaining each party’s view of the case, must be submitted—first by the petitioner putting forth his or her case, then by the respondent. After initial briefs have been filed, both parties may file subsequent briefs in response to the first. Likewise, people and groups that are not party to the case but are interested in its outcome may file an amicus curiae (“friend of the court”) brief giving their opinion, analysis, and recommendations about how the Court should rule. Interest groups in particular can become heavily involved in trying to influence the judiciary by filing amicus briefs—both before and after a case has been granted cert . And, as noted earlier, if the United States is not party to a case, the solicitor general may file an amicus brief on the government’s behalf.
With briefs filed, the Court hears oral argument s in cases from October through April. The proceedings are quite ceremonial. When the Court is in session, the robed justices make a formal entrance into the courtroom to a standing audience and the sound of a banging gavel. The Court’s marshal presents them with a traditional chant: “The Honorable, the Chief Justice and the Associate Justices of the Supreme Court of the United States. Oyez! Oyez! Oyez! [Hear ye!] All persons having business before the Honorable, the Supreme Court of the United States, are admonished to draw near and give their attention, for the Court is now sitting. God save the United States and this Honorable Court!” 58 It has not gone unnoticed that the Court, which has defended the First Amendment’s religious protection and the traditional separation of church and state, opens its every public session with a mention of God.
During oral arguments, each side’s lawyers have thirty minutes to make their legal case, though the justices often interrupt the presentations with questions. The justices consider oral arguments not as a forum for a lawyer to restate the merits of the case as written in the briefs, but as an opportunity to get answers to any questions they may have. 59 When the United States is party to a case, the solicitor general (or one of the solicitor general's assistants) will argue the government’s position; even in other cases, the solicitor general may still be given time to express the government’s position on the dispute.
When oral arguments have been concluded, the justices have to decide the case, and they do so in conference , which is held in private twice a week when the Court is in session and once a week when it is not. The conference is also a time to discuss petitions for certiorari , but for those cases already heard, each justice may state their views on the case, ask questions, or raise concerns. The chief justice speaks first about a case, then each justice speaks in turn, in descending order of seniority, ending with the most recently appointed justice. 60 The judges take an initial vote in private before the official announcement of their decisions is made public.
Oral arguments are open to the public, but cameras are not allowed in the courtroom, so the only picture we get is one drawn by an artist’s hand, an illustration or rendering. Cameras seem to be everywhere today, especially to provide security in places such as schools, public buildings, and retail stores, so the lack of live coverage of Supreme Court proceedings may seem unusual or old-fashioned. Over the years, groups have called for the Court to let go of this tradition and open its operations to more “sunshine” and greater transparency. Nevertheless, the justices have resisted the pressure and remain neither filmed nor photographed during oral arguments. 61


8.17C: Fungi Habitat, Decomposition, and Recycling
- Explain the roles played by fungi in decomposition and recycling
Fungi & Their Roles as Decomposers and Recyclers
Fungi play a crucial role in the balance of ecosystems. They colonize most habitats on earth, preferring dark, moist conditions. They can thrive in seemingly-hostile environments, such as the tundra. However, most members of the Kingdom Fungi grow on the forest floor where the dark and damp environment is rich in decaying debris from plants and animals. In these environments, fungi play a major role as decomposers and recyclers, making it possible for members of the other kingdoms to be supplied with nutrients and to live.
The food web would be incomplete without organisms that decompose organic matter. Some elements, such as nitrogen and phosphorus, are required in large quantities by biological systems; yet, they are not abundant in the environment. The action of fungi releases these elements from decaying matter, making them available to other living organisms. Trace elements present in low amounts in many habitats are essential for growth, but would remain tied up in rotting organic matter if fungi and bacteria did not return them to the environment via their metabolic activity.
The ability of fungi to degrade many large and insoluble molecules is due to their mode of nutrition. As seen earlier, digestion precedes ingestion. Fungi produce a variety of exoenzymes to digest nutrients. These enzymes are either released into the substrate or remain bound to the outside of the fungal cell wall. Large molecules are broken down into small molecules, which are transported into the cell by a system of protein carriers embedded in the cell membrane. Because the movement of small molecules and enzymes is dependent on the presence of water, active growth depends on a relatively-high percentage of moisture in the environment.
As saprobes, fungi help maintain a sustainable ecosystem for the animals and plants that share the same habitat. In addition to replenishing the environment with nutrients, fungi interact directly with other organisms in beneficial, but sometimes damaging, ways.
Key Points
- Aiding the survival of species from other kingdoms through the supply of nutrients, fungi play a major role as decomposers and recyclers in the wide variety of habitats in which they exist.
- Fungi provide a vital role in releasing scarce, yet biologically-essential elements, such as nitrogen and phosphorus, from decaying matter.
- Their mode of nutrition, which involves digestion before ingestion, allows fungi to degrade many large and insoluble molecules that would otherwise remain trapped in a habitat.
Key Terms
- decomposer : any organism that feeds off decomposing organic material, especially bacterium or fungi
- exoenzyme : any enzyme, generated by a cell, that functions outside of that cell
- saprobe : an organism that lives off of dead or decaying organic material


5.5: The Root
Root is a latest evolutionary innovation in the vegetative plant anatomy. Many “primitive” plants (all mosses and even some ferns like Psilotum ) do not have roots; some flowering water plants like the> rootless duckweed ( Wolffia ) or the coontail ( Ceratophyllum ) have also reduced their roots. However, large homoiohydric plants need the constant supply of water and minerals, and this evolutionary challenge was responded with appearance of the root system.
The Root in an axial organ of plant with geotropic growth . One of root functions is to supply anchorage of the plant body in soil or on various surfaces. Other functions include water and mineral absorption and transport, food storage, and communication with other plants.
Morphology of the Root
There are two types of root systems. The first is a fibrous root system which has multiple big roots that branch and form a dense mass which does not have a visible primary root (“grass-like”). The other is the tap root system which has one main root that has branching into lateral roots (“carrot-like”).
Along with having different systems, there are different types of roots: primary root originated from the root of the seedling, secondary (lateral) roots originate from the primary roots, and adventitious roots originate on stems (sometimes also on leaves), the example are prop roots of screw pine ( Pandanus ).
Roots employ many different modifications which help to protect, interact and storage. For example, roots of parasitic plants are modified into haustoria which sink themselves into the vascular tissue of a host plant and live off of the host plant’s water and nutrients.
Roots of mangroves (plants growing in ocean coastal swamps) are frequently modified into supportive aerial roots (“legs”). Since these swamp plants need oxygen to allow cell respiration in underground parts, there are pneumatophores , specialized roots which grow upward (!) and passively catch the air via multiple pores. Plants which grow on sand (psammophytes, see above) have another problem: their substrate constantly disappears. To avoid this, plants developed contractile roots which may shorten and pull plant body deeper into the sand.
Some orchid roots are green and photosynthetic (Figure \(\PageIndex{3}\))! However, as a rule, root is the heterotrophic organ, because root cells have no access to the light.
Root nodules present on the roots of nitrogen-fixing plants, they contain bacteria capable to deoxidize athmospheric nitrogen into ammonia: N\(_2\) \(\rightarrow\) NH\(_3\). Root nodules contain also hemoglobin-like proteins which facilitate nitrogen fixation by keeping oxygen concentration low. Nitrogen-fixing plants are especially frequent among faboid rosids : legumes (Leguminosae family) and many other genera (like alder, Alnus , or Shepherdia , buffaloberry) have root nodules with bacteria. Some other plants (mosquito fern, Azolla and dinosaur plant, Gunnera ) employ cyanobacteria for the same purpose.
Mycorrhiza is a root modification started when fungus penetrates root and makes it more efficient in mineral and water absorption: it will exchange these for organic compounds. In addition to mycorrhizal fungi, endophytic fungi inhabit other plant organs and tissues.
Anatomy of the Root
On the longitudinal section of young growing root, there are different horizontal layers, zones: root cap covering division zone , elongation zone , absorption zone , and maturation zone (Figure \(\PageIndex{4}\)). The root cap protects the root apical meristem (RAM), which is a group of small regularly shaped cells. A small, centrally located part of the RAM is the quiescent center where initial cells divide and produce all other cells of root. Root cap is responsible for the geotropic growth, if the root tip comes into contact with a barrier, root cap will feel it and will grow on a different direction to go around it.
The elongation zone is where the cells start to elongate, giving it length. The absorption zone where the rhizodermis tissue (root hairs) develops and where water and nutrients are absorbed and brought into the plant. Within the maturation zone , root hairs degrade, many cells start to acquire secondary walls and lateral roots develop (Figure \(\PageIndex{4}\)).
On the cross-section of the root made within absorption zone, the first tissue is the rhizodermis, which is also known as the root epidermis, then cortex, which segregates external exodermis and internal endodermis one-cellular layers, and vascular cylinder (Figure \(\PageIndex{5}\) ). Typically, roots have no pith. In some cases (for example, in orchids), cortex may give multi-layered velamen (see above), another absorption tissue.
Vascular cylinder is located in the center of the root, it contains the pericycle which is made of mostly parenchyma and bordering endodermis. Pericycle cells may be used for storage, they contribute to the vascular cambium, and initiate the development of lateral roots. Consequently, lateral roots are developing endogenously and break tissues located outside, like aliens in the famous movie. Root phloem is arranged in
several strands whereas xylem typically has a radial, sometimes star-shaped structure with few rays (Figure \(\PageIndex{6}\)). In the last case, phloem strands are located between rays of xylem.
Root tissues develop in the way similar to stem, RAM gave rise to ground meristem, procambium, and the protoderm, which in turn make all primary tissues mentioned above. Later, pericycle develops into lateral roots or the vascular cambium which in turn produces into the secondary xylem and phloem. The secondary root is similar to secondary stem (see below).
Water and Sugar Transportation in Plants
Plants need water to supply photosynthesis (the oxygen is from water!), to cool down via transpiration, and to utilize diluted microelements. Dead velamen (paper-like), rhizoids (hair-like), and living rhizodermis (rhizoderm) are responsible for water uptake.
In rhizodermis, root hairs increase the surface area where the plant has to absorb the nutrients and water. To take water, hair cells increase concentration of organic chemicals (the process which needs ATP) and then use osmosis. There are two ways that water transport may go: apoplastic or symplastic. Apoplastic transport moves water through the cell walls of cortex: from the rhizodermis to the endodermis. Endodermis cell walls bear Casparian strips (rich of hydrophobic suberin and lignin) which prevent the water from passing through the cell wall and force symplastic transport (Figure \(\PageIndex{7}\)) through cytoplasms and plasmodesmata. Symplastic transport there is directed to the center of root only and requires ATP to be spend.
By pumping water inside vascular cylinder and not letting it back, endodermis cells create the root pressure pressure force made solely by roots (Figure \(\PageIndex{8}\)). It is easy to observe on tall herbaceous plants cut near the ground: drops of water will immediately appear on the cutting. Inside tracheary elements of xylem, water moves with the root pressure, capillary force and the sucking pressure of transpiration. The latter means that water column does not want to break and if water disappears from the top (stomata on leaves), it will move water inside plant. The main direction of water movement is from roots to leaves, i.e. upwards.
Products of photosynthesis (sugars) are moving inside living cells of phloem; these cells (sieve tubes) use only symplastic transport to distribute glucose and other organic compounds among all organs of plants. In fact, phloem transports these components in all directions: to the flowers (usually upwards), and at the same time to the roots (usually downwards).


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14: Disease and Epidemiology (Part B)
Week 9
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BIOL 342: The New Plagues - New and Ancient Infectious Diseases Threatening World Health (Hughes)
Week 9
14: Disease and Epidemiology (Part B)
14.1: The Language of Epidemiologists
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14.1: The Language of Epidemiologists
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Goodyear AZ is one of the fastest growing cities in the nation according to the census bureau. In 2012, the population was about 72,800. The city’s population grew by 3800 people from 2012 to 2013. If the growth keeps up in a linear fashion, create a population model for Goodyear. How many people will live there in 10 years? How many people will live there in 50 years? (U.S. Census, 2014)
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Gilbert AZ is one of the fastest growing cities in the nation according to the census bureau. In 2012, the population was about 229,800. The city’s population grew by 9200 people from 2012 to 2013. If the growth keeps up in a linear fashion, create a population model for Gilbert. How many people will live there in 10 years? How many people will live there in 50 years? (U.S. Census, 2014)
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Apache County AZ, is shrinking according to the census bureau. In 2012, the population was about 71,700. The county’s population decreased by 1147 people from 2012 to 2013. If the decline is linear, create a population model for Apache County. How many people will live there in 10 years? How many people will live there in 50 years? (Kiersz, 2015)
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Cochise County AZ, is shrinking according to the census bureau. In 2012, the population was about 129,472. The county’s population decreased by 2600 people from 2012 to 2013. If the decline is linear, create a population model for Cochise County. How many people will live there in 10 years? How many people will live there in 50 years? (Kiersz, 2015)
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Mohave County AZ, is shrinking according to the census bureau. In 2012, the population was about 203,030. The county’s population decreased by 1200 people from 2012 to 2013. If the decline is linear, create a population model for Mohave County. How many people will live there in 10 years? How many people will live there in 50 years? (Kiersz, 2015)
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The 2012 Kia Sedona LX has one of the largest depreciation values of any car. Suppose a 2012 Kia Sedona sold for $24,900, and its value depreciates by $3400 per year. Assuming the depreciation is linear, find a model for the depreciation. How much is the car worth in five years? How much is the car worth in 10 years? When is it worth nothing? (Fuscaldo, n.d.)
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The 2013 Chevy Impala has one of the largest depreciation values of any car. Suppose a 2013 Chevy Impala sold for $27,800 and its value depreciates by $3600 per year. Assuming the depreciation is linear, find a model for the depreciation. How much is the car worth in five years? How much is the car worth in 10 years? When is it worth nothing? (Fuscaldo, n.d.)
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The 2013 Jaguar XJ AWD has one of the largest depreciation values of any car. Suppose a 2013 Jaguar XJ AWD sold for $74,500 and its value depreciates by $10,400 per year. Assuming the depreciation is linear, find a model for the depreciation. How much is the car worth in five years? How much is the car worth in 10 years? When is it worth nothing? (Fuscaldo, n.d.)
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The 2012 Jeep Liberty Limited Sport 2WD has one of the largest depreciation values of any car. Suppose a 2012 Jeep Liberty Limited Sport 2WD sold for $23,400 and its value depreciates by $3,040 per year. Assuming the depreciation is linear, find a model for the depreciation. How much is the car worth in five years? How much is the car worth in 10 years? When is it worth nothing? (Fuscaldo, n.d.)
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Suppose that in January, the maximum water depth at Lake Powell, Arizona was 528 feet. The water evaporates at an average rate of 1.2 feet per month. Find a model for the rate at which the water evaporates. If it does not rain at all, what will be the depth of Lake Powell in May and in September?
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Suppose that the maximum water depth at Lake Tahoe, California in 2014 was 1644 feet. Because of the drought, the water level has been decreasing at an average rate of 6.2 feet per year. Find a model for the rate at which the water level decreases. If it there is no precipitation at all, what will be the depth of Lake Tahoe be in two years, and in five years?
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Suppose the homes in Arizona have appreciated an average of 8% per year in the last five years. If the average home in a suburb sold for $225,000 in 2010, create a model for the home prices in the suburb. How much would this home be worth in 2015?
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Suppose the homes in Massachusetts have appreciated an average of 13% per year in the last five years. If the average home in a suburb sold for $205,000 in 2010, create a model for the home prices in the suburb. How much would this home be worth in 2015?
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Suppose the homes in Michigan have depreciated an average of 17% per year in the last five years. If the average home in a suburb sold for $215,000 in 2010, create a model for the home prices in the suburb. How much would this home be worth in 2015?
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Suppose the homes in Nevada have depreciated an average of 15% per year in the last five years. If the average home in a suburb sold for $318,000 in 2010, create a model for the home prices in the suburb. How much would this home be worth in 2015?
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The cost of a home in Flagstaff AZ was $89,000 in 1992. In 2007, the same home appraised for $349,000. Assuming the home value grew according to the exponential growth model, find the annual growth rate of this home over this 15-year period. If the growth continued at this rate, what would the home be worth in 2020?
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The cost of a home in Bullhead City AZ was $109,000 in 1992. In 2007, the same home appraised for $352,000. Assuming the home value grew according to the exponential growth model, find the annual growth rate of this home over this 15-year period. If the growth continued at this rate, what would the home be worth in 2020?
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The population of West Virginia is in decline. The population in 2014 was 1,850,326 and the population had decreased by 0.14% from 2010. How many people were living in West Virginia in 2010? Create a model for this population. If the decline continues at this rate, how many people will reside in West Virginia in 2020? (Wikipedia, n.d.)
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Assume that the population of Arizona grew by 2.4% per year between the years 2000 to 2010. The number of Native American living in Arizona was 257,426 in 2010. How many Native Americans were living in Arizona in 2000? Create a model for this population. If the growth continues at this rate, how many Native Americans will reside in Arizona in 2020?
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Assume the population of the U.S. grew by 0.96% per year between the years 2000 and 2010. The number of Hispanic Americans was 55,740,000 in 2010. How many Hispanic Americans were living in the U.S. in 2000? Create a model for this population. If the growth continues at this rate, how many Hispanic Americans will reside in The U.S. in 2020?
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Assume the population of Michigan decreased by 0.6% per year between the years 2000 to 2010. The population of Michigan was 9,970,000 in 2010. How many people were living in Michigan in 2000? Create a model for this population. If the growth continues at this rate, how many people will reside in Michigan in 2020?
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The doubling time of a population of aphids is 12 days. If there are initially 200 aphids, how many aphids will there be in 17 days?
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The doubling time of a population of rabbits is six months. If there are initially 26 rabbits, how many rabbits will there be is 17 months?
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The doubling time of a population of shrews is three months. If there are initially 32 shrews, how many shrews will there be is 21 months?
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The doubling time of a population of hamsters is 1.2 years. If there are initially 43 hamsters, how many hamsters will there be is 7 years?
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A certain cancerous tumor doubles in size in three months. If the initial size of the tumor is two cells, how many months will it take for the tumor to grow to 60,000 cells? How many cells will there be in 1.5 years? In three years?
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A certain cancerous tumor doubles in size in 1.5 months. If the initial size of the tumor is eight cells, how many months will it take for the tumor to grow to 40,000 cells? How many cells will there be in six months? In 2.5 years?
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A bird population on a certain island has an annual growth rate of 1.5% per year. Approximate the number of years it will take the population to double. If the initial population is 130 birds, use it to find the bird population of the island in 14 years.
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The beaver population on Kodiak Island has an annual growth rate of 1.2% per year. Approximate the number of years it will take the population to double. If the initial population is 32 beavers, use it to find the population of beavers on the island in 20 years.
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The black-footed ferret population in Arizona has an annual growth rate of 0.5% per year. Approximate the number of years it will take the population to double. If the initial population is 230 ferrets, use it to find the ferret population in AZ in 12 years.
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The Mexican gray wolf population in southern Arizona increased from 72 individuals to 92 individuals from 2012 to 2013. What is the annual growth rate? Approximate the number of years it will take the population to double. Create the doubling time model and use it to find the population of Mexican gray wolves in 10 years.
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There is a small population of Sonoran pronghorn antelope in a captive breeding program on the Cabeza Prieta National Wildlife Refuge in southwest Arizona. Recently, the population increased from 122 individuals to 135 individuals from 2012 to 2013. Approximate the number of years it will take the population to double. Create the doubling time model and use it to find the population of Sonoran pronghorn antelope in 10 years.
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Lead-209 is a radioactive isotope. It has a half-life of 3.3 hours. Suppose that 56 milligrams of this isotope is created in an experiment, how much is left after 12 hours?
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Titanium-44 has a half-life of 63 years. If there is 560 grams of this isotope, how much is left after 1200 years?
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Uranium-232 has a half-life of 68.9 years. If there is 160 grams of this isotope, how much is left after 1000 years?
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Nickel-63 has a half-life of 100 years. If there is 16 grams of this isotope, how much is left after 145 years?
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Radium-226 has a half-life of 1600 years. If there is 56 grams of this isotope, how much is left after 145,000 years?
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The population of wild desert tortoises is decreasing by 72% per year. Approximate the half-life for this population. If there are currently 100,000 tortoises left in the wild, how many will remain in 20 years?
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The population of pygmy owls is decreasing by 4.4% per year. Approximate the half-life for this population. If there are currently 41 owls left in the wild, how many will remain in five years?
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Radioactive carbon-14 is used to determine the age of artifacts because it concentrates in organisms only when they are alive. It has a half-life of 5730 years. In 2004, carbonized plant remains were found where human artifacts were unearthed along the Savannah River in Allendale County. Analysis indicated that the plant remains contained 0.2% of their original carbon-14. Estimate the age of the plant remains. (Wikipedia, n.d.)
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The population of a bird species on an island grows according to the logistic model below. \[P(t)=\dfrac{43,240}{1+12 e^{-0.05 t}}\nonumber \]Identify the initial population. What will be the bird population in five years? In 150 years? In 500 years? What is the carrying capacity of the bird population on the island?
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Suppose the population of students at Arizona State University grows according to the logistic model below with the initial population taken from 2009. \[P(t)=\dfrac{85,240}{1+0.6 e^{-0.15 t}} \nonumber \]Identify the initial population. What will be the campus population in five years? What will be the population in 20 years? What is the carrying capacity of students at ASU?
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Suppose the population of students at Ohio State University grows according to the logistic model below with the initial population taken from 1970. \[P(t)=\dfrac{90,000}{1+4 e^{-0.06 t}} \nonumber \]Identify the initial population. What will be the campus population in five years? What will be the population in 20 years? What is the carrying capacity of students at OSU?
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Suppose that in a certain shrimp farm, the shrimp population is modeled by the logistic model below where t is measured in years. \[P(t)=\dfrac{120,000}{1+25 e^{-0.12 t}} \nonumber \]Find the initial population. How long will it take for the population to reach 6000 shrimp? What is the carrying capacity of shrimp on the farm?
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Suppose that in a certain oyster farm, the oyster population is modeled by the logistic model below where
t
is measured in years. \[P(t)=\dfrac{18,000}{1+19 e^{-0.36 t}} \nonumber \]Find the initial population. How long will it take for the population to reach 2000 oysters? What is the carrying capacity of oysters on the farm?


6.2: Word Components Related to the Male Reproductive System
This section will describe common word components related to the male reproductive system system. These word components help build definitions for many medical terms. Other common prefixes are described in Chapter 1.3 , and common suffixes are described in Chapter 1.5 .
COMMON PREFIXES RELATED TO THE MALE REPRODUCTIVE SYSTEM
- a- : Absence of, without
- an- : Absence of, without
- crypt- : Hidden
- dys- : Painful, difficult
- epi- : Above
- hyper- : Above, excessive
- hypo- : Below
- par- : Near
- trans- : Through, across, beyond
COMMON WORD ROOTS WITH A COMBINING VOWEL RELATED TO THE MALE REPRODUCTIVE SYSTEM
- andr /o: Male
- balan /o: Glans penis
- epididym /o: Epididymis
- gonad /o: Gonad
- orch /o: Testis, testicle
- orchi /o: Testis, testicle
- orchid /o: Testis, testicle
- pen /i: Penis
- phall /o: Penis
- posth /o: Prepuce, foreskin
- preputi /o: Prepuce, foreskin
- prostat /o: Prostate gland
- scrot /o: Scrotum
- semin /i: Semen
- sperm /o: Sperm, spermatozoon
- spermat /o: Sperm, spermatozoon
- test /o: Testis, testicle
- testicular /o: Testis, testicle
- urethr /o: Urethra
- vas /o: Vas deferens, vessel, duct
- vesicul /o: Seminal vesicle
COMMON SUFFIXES RELATED TO THE MALE REPRODUCTIVE SYSTEM
- -al : Pertaining to
- -algia : Pain
- -ar : Pertaining to
- -cision : Processing of cutting
- -ectomy : Excision or surgical removal
- -genesis : Beginning, development, or production
- -gram : Record
- -graphy : Process of recording
- -ia : Diseased state, abnormal state, condition of, condition
- -ic : Pertaining to
- -ism : State of, condition
- -itis : Inflammation
- -logy : Study of
- -lysis : Loosening, dissolution, separating
- -oma : Tumor, mass
- -ous : Pertaining to
- -pathy : Disease
- -pexy : Surgical fixation, suspension
- -plasia : Development, growth
- -plasty : Surgical repair
- -rrhea : Flow, discharge
- -sis : Condition
- -stomy : Creation of new opening, process of new opening
- -tomy : Cut into, incision


5.1.3H: Social Networks
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Learning Objectives
- Assess the role of social networks in the socialization of people
A social network is a social structure that exists between actors—individuals or organizations. A social network indicates the way that people and organizations are connected through various social familiarities, ranging from casual acquaintance to close familial bonds. Social networks are composed of nodes and ties. The person or organization participating in the network is called a node. Ties are the various types of connections between these nodes. Ties are assessed in terms of strength. Loose connections, like mere acquaintances, are called weak ties. Strong ties, like family bonds are called strong ties.
Shape and Size
The shape and size of social networks influence their utility for their nodal participants. Smaller, tighter networks composed of strong ties behave differently than larger, looser networks of weak ties. The looser and larger the network, the more likely nodes are to introduce new ideas and opportunities to their members. Participants in smaller networks are more likely to share values and information, increasing efficiency, but decreasing creativity.
Small World Phenomenon
The small world phenomenon is the hypothesis that the chain of social acquaintances required to connect one arbitrary person to another arbitrary person anywhere in the world is generally short. The concept gave rise to the famous phrase “six degrees of separation” after a 1967 small world experiment by psychologist Stanley Milgram which found that two random US citizens were connected by an average of six acquaintances.
Facebook as a Social Network : This video discusses the merits and problems with Facebook as a social network.
The study of social networks is called either social network analysis or social network theory. Research has indicated that social networks operate on many levels—from familial to national—and play a critical role in determining the ways that problems are solved, the way organizations are run, and the degree to which individuals succeed in achieving their goals. Social network theory argues that individual traits and characteristics usually presumed to have significance actually matter far less than an individual’s relationship and ties to other actors in a network. Critics argue that this perspective diminishes the power and agency of the individual. Despite these criticisms, sociologists study social networks because of their influence on individuals. Social networks are seen as the basic tool individuals use to connect to society.
Key Points
- A social network is comprised by various nodes and the ties that connect them.
- Nodes can be individuals or organizations.
- Ties are the various types of connections these nodes. Ties are assessed in terms of strength. Loose connections, like mere acquaintances, are called weak ties. Strong ties, like family bonds are called strong ties.
- The study of networks is called either social network analysis or social network theory.
- The small world phenomenon is the hypothesis that the chain of social acquaintances required to connect one arbitrary person to another arbitrary person anywhere in the world is generally short. The concept gave rise to the phrase “six degrees of separation” after Stanley Milgram’s 1967 experiment.
Key Terms
- Ties : They are the various types of connections between nodes.
- node : They are the individual actors within the networks, and ties are the relationships between the actors.
- Social Network Analysis : It is the study of social networks