“Cooking Demo with Chef Maurice”
Why Use Props?
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To engage the audience
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To focus attention
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To make your message more memorable
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To retain the audience’s attention
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To emotionally impact the audience
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To break away from using slides
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To help the audience understand
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To demonstrate how to do things
Best Practices on How to Use Props
Select your props with care.

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Proofread/check for errors (often better to get a different set of eyes on them as you may gloss over the errors).
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Make sure your prop is not offensive.
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Consider how you will carry your prop to and from the speaking venue.
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Make sure your prop is not offensive.
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Consider set-up and take-down time (if working with food, glue, or other messy items, bring wipes and a trash bag).
Practice with your props.

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Be able to smoothly show and put away your prop.
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Have a plan for how to hide the prop until you need it.
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Make eye contact with your audience while working with your prop.
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Place your prop where you can easily reach it.
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In demonstration speeches, make sure everything is opened (it is hard to open cream cheese while speaking).

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Put the prop away after using it.
Have a backup plan in case the prop does not work.
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Bring tape in case you have to hang something up.
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Have whiteboard markers in case you need to write on the board.
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Practice with a clicker and your prop so you know how to work them together.
Additional Thoughts on Props
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Include reminders on your notecards for when to use the prop.
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If your prop involves a volunteer, make sure they know what is expected.
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Do not pass items around for the audience to see, it is too distracting.

Time to watch: 2:20-4:00
Props Help Demonstrate How Something Works
It can be difficult to envision how things work with only an explanation. In this speech, Michael Pritchard not only tells us, but he also demonstrates for us how the water filter works. He starts by taking dirty water and makes it even dirtier. The dirty water causes some people to have a physical reaction. This makes it even more memorable when he finally cleans the water and then hands it to someone to drink.
Time to watch: 3:00-5:30
Props Can Be Used to Prove a Point
When writing this chapter on props, I asked public speaking teachers to give me their best examples of how students used props effectively and Mike Fleming shared this story.
When I first began teaching, I had to shadow someone who was currently teaching. One Saturday morning, one of the students had a large, 50-pound sack of dry dog food. When called, she went up, and put the bag on the corner of the desk, went around it, and began her speech. She started talking about her wedding. She explained how she was a newlywed. She told of the importance, to her, of fitting into her wedding dress, and of all she had gone through to make that happen. She spoke of having been chubby her entire life, etc. At the very end of her speech, after telling us that she had accomplished her goal, and had fit into her dress, she stepped around the desk, put her arm around the bag of dog food, hoisted it onto her hip, and told us that if she had stepped onto a scale just then, the scale would have showed what she had weighed, at the start of her journey. She put the bag back on the desk and said, “But not anymore! Mike Fleming.
Speaker Kenny Nguyen uses the prop of a sword and a shield to anchor his message.
Watch from 8.59 to the end. He doesn’t use the props right away but I wanted you to see the context so I backed up the video a little. Notice how he has the prop out of the way until he needs it to solidify his point.
Props Can Carry the Theme
In this graduation speech, Valedictorian Carl Aquino uses a Rubik’s cube to talk about high school. Watch how he uses it to show the difference between high school and college.
Props Can Be Used to Teach Complex Concepts
Dan Burns teaches other teachers how to demonstrate spacetime warping. Does this help you understand the scientific principles? I know I learned a lot from this. Notice how he talks as he demonstrates. He could improve by having some of these objects a little closer so there isn’t an awkward pause as he gets his balls.
Watch from the beginning
You Can Be the Prop
Lizzy Velasquez talks about a syndrome she has. In this speech, she is the prop. She draws attention to her eyes and then highlights the great things about her eyes.
Time to watch: 0-2:00
Props Can Help Tell a Story
Aimee Mullins engages the audience by telling a story of how children reacted to seeing all her prosthetic legs. As we look at the props on the stage, we can better imagine the reactions of the children.
Time to watch: 0-2:14
Props Can Enhance Persuasion
Watch as Mark Scarpitti illustrates the benefits of no-till soil. Notice how he engages his audience by asking them questions as he demonstrates; it really helps engage his audience. He has all of his props set up before he begins and they are set out in a way that they are easy to see. He wisely uses volunteers which further engages the group. By showing instead of just telling, he makes a convincing case for no till-soil.
 In this video, Elon Musk, with the help of an assistant, illustrates the Cybertruck’s load mode.
Time to watch: 12:00-13:45
Props Can Illustrate Complex Concepts
Frances Chan, Christian Pastor, illustrates the concept of “eternity” to a church audience with, of all things, a rope.
Time to watch: 0-2:00
Props to Help the Audience Relate to Numbers and Think Deeply About a Concept
Jamie Oliver is not only passionate about food, he is passionate about teaching people to eat healthier. Watch as he illustrates how much sugar is in milk. As you watch the video, notice how he has a volunteer bring his prop on the stage at just the right time. As he dumps one cup at a time on the floor, we begin to see the problem. Finally, when he dumps the wheelbarrow of sugar on the floor and then dramatically tosses it in the air, we begin to sense the urgency of the problem.
Time to Watch: 12:00-14:00
Props Can Engage the Audience’s Attention
Andrea Schiefelbein uses humor and some creative poster usage at a High School National Speech and Debate Championship. Notice how she creatively uses the poster board in layers. Pay attention to how she has just plain black poster board when she doesn’t need us to see a picture. Finally, watch as she uses the genderbread man to draw us and she causes us to think as we watch her add pieces to the poster.
Watch from 0-4:00
Posters Can Be Used Instead of Slides to Draw the Audience’s Attention
Dave Lieber, a columnist for
The Dallas Morning News,
talks about trying to adapt to Texas culture while teaching the audience how to tell the story. Notice how effective his poster is as opposed to using a slide show. Ask yourself, would it have been as engaging if he would have shown us a slide of the dog?
Time to Watch: 12:50-14:00
Props Can Be Used With Slides to Draw the Audience’s Attention
Daniel Kraft demonstrates the Marrow Minor. He uses four props, slides, and a video in four minutes. Watch as he masterfully negotiates all his visuals while maintaining a conversational tone with the audience.
Check Out This Article on How Politicians Use Props
Business Insider Looked at
10 Wild Props Used by Congressional Members
that I thought you would enjoy. (My personal favorite is Reagan riding a velociraptor–I included it here for your viewing pleasure) Watch this short video clip as Republican Senator Mike Lee makes fun of the Green New Deal using Reagan on a dinosaur, Star Wars, and Sharknado.
MIT Professor Patrick Winston gives a lecture on how to use props. He goes into detail about why he thinks props work. Watch for yourself, the answer might surprise you. Watch from 13 to 24 minutes.
Key Takeaways
Remember This!
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Props can help the audience pay attention, understand concepts, and remember your information.
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Props should enhance your message.
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The prop should be large enough to see.
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Practice with your props to seamlessly integrate them into your speech.
Please share your feedback, suggestions, corrections, and ideas
I want to hear from you.
Do you have an activity to include?
Did you notice a typo that I should correct?
Are you planning to use this as a resource and do you want me to know about it?
Do you want to tell me something that really helped you?
Click here to share your feedback.
Looking for More Information?
I didn’t want to overwhelm you with too many examples when you read the chapter, so I included some of the extra video clips, examples, and activities in a separate chapter.
Presentation Aids: Activities and Resources
Editorial note: For copyright considerations,
I have given you speech samples in their entirety. Showing only short clips violates the copyright privileges of those who graciously posted the speech videos. I have given you start and stop times to see the prop and how it is used. It will take you about 20 minutes to watch all the clips. Warning: these are interesting videos and it will be hard to watch only the suggested segment.
References
Aquino, C. (2011). The Valedictorian Speech that will change your life. [Video] YouTube.
https://www.youtube.com/watch?v=lCN6FjqDcHg
Standard YouTube License.
Armour, C. Schneid, S.D., Brandl, K. (2016). Writing on the board as students’ preferred teaching modality in a physiology course. Physiology.
https://doi.org/10.1152/advan.00130.2015
Burns, D. (2012). Gravity visualized. [Video] YouTube.
https://www.youtube.com/watch?v=MTY1Kje0yLg
Standard YouTube License.
Chan, F. (2010). Frances Chan-Rope illustration.[Video] YouTube.
https://www.youtube.com/watch?v=86dsfBbZfWs
Standard YouTube License.
Cnet. (2019). Watch Elon Musk announce the Tesla Cybertruck in 14 minutes. [Video] YouTube.
https://www.youtube.com/watch?v=464puoD09dM
Standard YouTube License.
Dlugan, A. (2013). How to choose and use speech props: A speaker’s guide.
http://sixminutes.dlugan.com/speech-props/ Standard YouTube License.
Gates, B. (2013). Mosquitos, malaria, and education. Ted. [Video] YouTube.
https://www.youtube.com/watch?v=ZLkbWUNQbgk
Standard YouTube License.
Kraft, S. (2009). A better way to harvest bone marrow. [Video] YouTube.
https://www.ted.com/talks/daniel_kraft_a_better_way_to_harvest_bone_marrow?utm_campaign=tedspread&utm_medium=referral&utm_source=tedcomshare
Standard YouTube License.
Lieber, D. (2013). The power of storytelling to change the world. Ted. [Video] YouTube.
https://youtu.be/6Bo3dpVb5jw
Standard YouTube License.
Lineham, D. 9n.d.). How to use props in presentations.
https://davelinehan.com/how-to-use-props-in-presentations/
Mullins, A. (2009). My 12 pair of legs. Ted. [Video] YouTube.
https://www.ted.com/talks/aimee_mullins_my_12_pairs_of_legs?utm_campaign=tedspread&utm_medium=referral&utm_source=tedcomshare
Standard YouTube License.
Nguyen, K. (2013). The art of saying no: Kenny Nguyen at TEDxLSU. [Video] YouTube.
https://www.youtube.com/watch?v=FtPRrn5nwAo&t=563s
Standard YouTube License.
Oliver, J. (2010). Teach every child about food. Ted. [Video] YouTube.
https://www.ted.com/talks/jamie_oliver_teach_every_child_about_food?language=en
Standard YouTube License.
Pritchard, M. (2009). [Video] YouTube. How to make filthy water drinkable. Ted.
https://www.ted.com/talks/michael_pritchard_how_to_make_filthy_water_drinkable?utm_campaign=tedspread&utm_medium=referral&utm_source=tedcomshare
Standard YouTube License.
Relman, E. (2019). A GOP senator brought a giant picture of Ronald Reagan riding a dinosaur to argue against Democrats’ Green New Deal. Here are 10 other wild props members have brought to the floor. Business Insider. [Video]
https://www.businessinsider.com/ranked-10-best-props-congress-2017-8?fbclid=IwAR2XRZC0VnjxMu6NqnjCAMBoDuaX2WS5Z7rYNtCEzPGMATsJkWhxh0WyRiE
Standard YouTube License.
Scarpitti, Ml (2011). Differences in tilled and no till soil.[Video] YouTube.
https://www.youtube.com/watch?v=q1aR5OLgcc0&feature=youtu.be
Standard YouTube License.
Schiefelbein, A. (2020). Anderea Schiefelbein “beyond pink and blue”-Informative Speaking. Nationals 2019. [Video] YouTube.
https://www.youtube.com/watch?v=rVBUarS1H7U
Standard YouTube License.
Taylor, J.B. (2008). My stroke of insight. TedTalk [Video] YouTube.
https://www.ted.com/talks/jill_bolte_taylor_my_stroke_of_insight
Standard YouTube License.
Valasquez, L. (2014). How do you define yourself. Ted [Video] YouTube.
https://www.youtube.com/watch?v=QzPbY9ufnQY
Standard YouTube License.
Valentin, C. (2015). Craig Valentine Speaks About His Nametag.[Video] YouTube.
https://www.youtube.com/watch?v=e_KRqkmPmag&feature=youtu.be
Standard YouTube License.
Winston, P. (2019). How to speak by Patrick Winston. [Video] YouTube.
https://www.youtube.com/watch?v=Unzc731iCUY
Standard YouTube License.
Zimmerman, J. (2017). How to “prop up” your next presentation. Presentation Guru.
https://www.presentation-guru.com/how-to-prop-up-your-next-presentation/#:~:text=In%20a%20presentation%2C%20props%20are,be%20handled%20by%20the%20presenter
.
Zimmer, J. (2011). Ten tips for using props in a presentation. Manner of speaking.
https://mannerofspeaking.org/2011/09/29/ten-tips-for-using-props-in-a-presentation/


11: Math Support for Statistics Last updated Save as PDF Page ID 128683 Larry Green Lake Tahoe Community College 11.2: Decimals Fractions and Percents 11.2.1: Comparing Fractions, Decimals, and Percents 11.2.2: Converting Between Fractions, Decimals and Percents 11.2.3: Decimals- Rounding and Scientific Notation 11.2.4: Using Fractions, Decimals and Percents to Describe Charts 11.3: The Number Line 11.3.1: Distance between Two Points on a Number Line 11.3.2: Plotting Points and Intervals on the Number Line 11.3.3: Represent an Inequality as an Interval on a Number Line 11.3.4: The Midpoint 11.4: Operations on Numbers 11.4.1: Area of a Rectangle 11.4.2: Factorials and Combination Notation 11.4.3: Order of Operations 11.4.4: Order of Operations in Expressions and Formulas 11.4.5: Perform Signed Number Arithmetic 11.4.6: Powers and Roots 11.4.7: Using Summation Notation 11.5: Sets 11.5.1: Set Notation 11.5.2: The Complement of a Set 11.5.3: The Union and Intersection of Two Sets 11.5.4: Venn Diagrams 11.6: Expressions, Equations and Inequalities 11.6.1: Evaluate Algebraic Expressions 11.6.2: Inequalities and Midpoints 11.6.3: Solve Equations with Roots 11.6.4: Solving Linear Equations in One Variable 11.7: Graphing Points and Lines in Two Dimensions 11.7.1: Finding Residuals 11.7.2: Find the Equation of a Line given its Graph 11.7.3: Find y given x and the Equation of a Line 11.7.4: Graph a Line given its Equation 11.7.5: Interpreting the Slope of a Line 11.7.6: Interpreting the y-intercept of a Line 11.7.7: Plot an Ordered Pair


12.2: Occupational Health Policy
Occupational health hazards have been recognized since antiquity, but it wasn’t until the industrial revolution that there was widespread awareness of the need to regulate workplaces. Initially these efforts were based on sanitation, cleanliness, and reducing worker injuries - which were common in many factories (Seabert et al., 2021). After decades of industrial tragedies including deaths nearly every other day in steel mills, a plethora of coal mine accidents, the Triangle Shirtwaist factory fire, the Hawk’s Nest Tunnel disaster, and others, worker’s unions and environmentalists worked together to lobby congress for worker’s protections in the 1960’s (Frumkin, 2016). The Occupational Safety and Health Act (OSH Act) has only been around for just over 50 years, as it was signed into law by President Richard Nixon in 1970. It began by setting standards for worker exposure to specific environmental hazards, such as asbestos, lead, and cotton dust. Since then more standards have been established to protect workers from injuries, bloodborne pathogens, and other environmental toxins (OSHA, n.d. -b). The OSH Act also established the Occupational Safety and Health Administration (OSHA) to set and enforce these standards, and the National Institute for Occupational Safety and Health (NIOSH) to conduct research and make recommendations for these health standards (Seabert et al., 2021). Because of these laws and oversight agencies, it is widely accepted that employers are responsible for providing “safe workplaces, free of recognized serious hazards” (Frumkin, 2016).
“This 2016 image depicted the process of hydraulic fracturing, or fracking, a 24/7 activity, and showed how the need for occupational health and safety never stops. NIOSH researchers from the Western States Division, and the Division of Applied Research and Technology, were the first to systematically document hazardous exposures to workers at fracking sites, including exposures to respirable crystalline silica (RCS), diesel particulate matter, and volatile organic compounds. This sand mover operator was monitoring the sand level in the blender tub, framed in the bottom left handrail. His half-face cartridge respirator may not have been providing a high enough assigned protection factor to protect him from the elevated concentration of RCS, to which he was exposed. This photograph was taken in Encinal, Texas, during a test of a NIOSH-developed engineering control, known as the NIOSH mini-baghouse retrofit assembly, installed to reduce RCS emissions.”
Prior to the industrial revolution, common law principles held the worker at fault for any injuries they received while on the job, and some employers went so far as to require “death contracts” as an acknowledgement of the employee of the potential dangers - and perhaps deadliness - of their work. In the late 19th century, Prussia was the first country to create worker’s liability and insurance laws in an effort to maintain the loyalty of the working class while squashing Marxist and socialist political movements. Other European countries and the U.S. followed suit, although it took until 1948 for the last state to enact worker’s compensation laws. While these laws did provide for monetary compensation in the form of employer-funded insurance policies, they also protected the companies from the threat of lawsuits (Guyton, 1999). Currently, each state in the U.S. has its own worker’s compensation system, rules, and regulations, which may cover or exclude certain injuries or illnesses (Frumkin, 2016). Notably, in many states, agricultural employers are exempt from the requirements to provide workers’ compensation, even though agricultural work is some of the most dangerous. Fourteen states (including California) do require workers’ compensation for agricultural businesses, and enforce penalties for non-compliance (Mikolajczyk, 2022).


1.45: The Sustainable Development Goals and pharmacy practice- a blueprint for health
At the end of this case, students will be able to:
- Recognize the impact of the SDGs on patient care
- Discuss the relationship between the SDGs and the role of the pharmacists in patient care and achieving public health goals
- Examine the role of SDGs and their targets in specific patient case scenarios
Introduction
In 2015, the Sustainable Development Goals (SDGs) were established and adopted by all United Nations (UN) Member States as part of the 2030 Agenda for Sustainable Development. 1 The SDGs consist of 17 main goals, each with multiple specified targets, were developed based on decades of previous global health work by individual countries and the UN, including the Millennium Development Goals. 2 They serve as a blueprint for global health, recognizing that tackling problems in climate change, education, inequality, and economic growth are important and go hand in hand with directly tackling problems in improving health.
The 17 goals consist of: (1) no poverty, (2) zero hunger, (3) good health and well-being, (4) quality education, (5) gender equality, (6) clean water and sanitation, (7) affordable and clean energy, (8) decent work and economic growth, (9) industry, innovation and infrastructure, (10) reduced inequalities, (11) sustainable cities and communities, (12) responsible consumption and production, (13) climate action, (14) life below water, (15) life on land, (16) peace, justice and strong institutions, and (17) partnerships to achieve the goals. 2 Together, the 17 SDGs have 169 targets to achieve by 2030. 2
The SDGs cover a broad range of topic areas, and in many instances, the goals and their targets may seem unrelated to what a pharmacist does on a daily basis. Despite this, a closer look at the relationships between the SDGs and the role of pharmacists in patient care will show that achieving public health goals do impact the patients that pharmacists interact with and are more intricately related than it may have first seemed. For example, SDG 6 focuses on clean water and sanitation, which from a bird’s eye view does not seem like it has to do with pharmacist direct patient care. However, understanding that lack of access to drinking water may prevent patients from being able to take their pills, and poor sanitation may result in infectious diseases that pharmacists will then have to work with physicians to treat. Additionally, SDG goals focused on economic growth such as SDG 8 (decent work and economic growth) can also be relevant to direct patient care because without employment and a means to make an income, patients often cannot afford medications that they need, resulting in uncontrolled disease states. Although only one of the SDGs directly addressed good health and well-being, many of the SDGs can influence how our patients present and what we can do to help them with their care.
Case
You are on an international APPE rotation providing medication therapy management (MTM) services alongside your preceptor in a rural village just outside the main city capital in a country in Southeast Asia. You are present as a student observer to learn more about how medications are managed for patients in this different cultural setting.
CC: “She says she’s here to begin medication services.”
Patient: DS is a 42-year-old Indian female (65 in, 82 kg) who was referred to you for MTM services. Her T2DM and asthma have been uncontrolled for many years, and the physicians are concerned about her worsening microvascular complications from persistently high sugars. Since her physicians were educated about pharmacist services, they have asked the pharmacist at the clinic to try and help manage her medications to better control her chronic diseases.
HPI: DS does not speak English and you are provided with a student translator to be able to understand the discussion during the visit. She does not have insurance and pays for everything out of pocket, with permission from her husband.
PMH: T2DM (for eight years); asthma (since age 10); PTSD (unknown duration)
FH: Unknown; she left her family at a young age in an arranged marriage and has not spoken to her parents since age eight.
SH:
- Denies alcohol or tobacco use
- Denies illicit drug use
Medications:
- Metformin 1000 mg BID
- Glipizide 10 mg daily
- Insulin glargine 25 units subcutaneously nightly
- Albuterol HFA 90 mcg inhaler 1-2 puffs every 4-6 hours as needed
Allergies: NKDA
Vitals: POC glucose at today’s visit 342 mg/dL
Labs:
- HgbA1c from 15 months ago 10.2%
- No other labs available due to limited resources for lab work in the clinic
ROS: Not performed at this visit
Surgical history: C-section delivery of 3rd child (five years ago)
SDH: DS has been married since the age of eight and lives in a rural village with limited clean water and electricity. Her family is very poor. She is a pescatarian with a diet that consists mainly of bread, beans, and any fish available, but since good fish from the market is expensive, she pays less for fish that locals catch from nearby streams and lakes, sometimes eating it without fully knowing what kind of fish it is. Her village is highly polluted mainly because there is no running water, no proper sanitation system for bathroom use, and air pollution from the main city reaches their small village leaving little clean air for breathing.
Additional context: Before the visit, you are informed by her physician that DS lives in an abusive marriage but since she has no means to provide for herself or her children, she continues to live at home with no intention of leaving her husband. Her husband has tight control over everything she does, and also keeps a close eye on what medications she is taking on a daily basis. She is not able to do much without being watched and if she is caught doing something her husband does not agree with, she is often physically and verbally abused.
Case Questions
Use the following website to assist in answer the following case questions: https://sdgs.un.org/
- The pharmacist begins by asking DS questions about her diabetes medications. She reports compliance on all her oral medications, but states she only takes her insulin sometimes. Upon further questioning, it is revealed that her home does not have running electricity, and she was taught that if it gets hot in her home, she must throw her insulin out. Her husband only gives her money to buy insulin once every three months, so after she disposes of it, she does not get another one for a while. What SDG(s) is/are related to this problem and achieving which SDG targets within this goal could help prevent this problem in the future?
- The pharmacist finds some pamphlets on lifestyle changes that can be helpful in controlling diabetes and provide them to DS to help her learn about diet and exercise recommendations. Upon receiving them, she states she never learned to read or write and hands the pamphlets back. What SDG(s) is/are related to this problem and achieving which SDG targets within this goal could help prevent this problem in the future?
- The pharmacist asks about DS’s PTSD and if she has ever taken anything for it. She states she has had it for a while and thinks it is because of the violence in her marriage. However, her husband does not believe there is anything wrong and will not allow her to take medications for a problem that “does not exist”. What SDG(s) is/are related to this problem and achieving which SDG targets within this goal could help prevent this problem in the future?
- At the end of the visit, the pharmacist asks DS if she has any questions about her medications. She states that all three of her children seem to have some learning deficits and is not sure why. She wants to know if there was any medication that they can be given. The pharmacist proceeds to discuss this with the physician since this is out of her scope of practice. The physician states that she has asked this question many times, but the answer is always no, there aren’t any medications that can be given. He proceeds to say that although there could be multiple causes, he thinks one main problem is that she is eating fish from bodies of water that are highly polluted with toxins such as Polychlorinated biphenyls (PCB), which could be causing harm to her children when she is pregnant. What SDG(s) is/are related to this problem and achieving which SDG targets within this goal could help prevent this problem in the future?
- What barriers now exist for managing this patient’s health conditions because above mentioned SDG goals have not been met?
- Which targets in SDG3 relate directly to the care you are trying to provide for DS?
- Recognizing the important role that SDG’s can play on patient care, what solutions (policies, programs, etc.) can you think of that may help to achieve any one or multiple of the SDG’s? Brainstorm a list and think about the applicability of these solutions to different countries around the world.
- In many instances, the best way to find solutions is to engage directly with the community you are trying to help. In what ways would you want to do this? Describe community engagement initiatives you would want to initiate to help advance an SDG or SDG target.
- Although it is important to understand how public health problems that are being tackled in the SDGs can directly impact patient care, there is also an ethical component that is important to recognize. What ethical problems do you note in this case and what do you think is the best way to tackle these issues?
Author Commentary
The SDGs represent a unified, worldwide front on tackling some of the world’s greatest public health challenges. As pharmacists, our direct patient care interactions in high-income countries may seem to have little to do with many of the SDGs and their targets, but it is imperative to realize that many of these goals are related to social determinants of health and impact how patients present to us as well as what barriers they have managing their own health.
Pharmacists and student pharmacists can and should be a part of the larger initiative to improve public health, particularly in reaching targets in SDG 3 (Good health and well-being: Ensure healthy lives and promote well-being for all at all ages), through patient education and being part of policy development in our country. Even though the SDGs and their targets are applicable across the world (and often may seem to be more important for developing countries), it is vital to recognize that public health efforts are needed everywhere, including the US, and particularly for populations who live in socioeconomically disadvantaged areas. The concept of local is global is very applicable as we aim and work to be part of the solution in attaining the targets set out in the SDGs.
Patient Approaches and Opportunities
SDGs should play a critical role in our approach to the provision of patient care across cultures and locations. It is imperative that pharmacists are aware of the various aspects of a patient’s life including social determinants of health that play a pivotal role in patient care, treatment, and ultimately health outcomes. Pharmacists have a duty to provide culturally respectful care, free from bias and saviorism. Pharmacists and pharmacy students should engage in cultural competency training and personal reflection to ensure they are not projecting unrecognized biases onto patients. Pharmacists should take advantage of opportunities to better understand the impact of culture and community on patient treatment through direct patient communication as well as immersion in the community wherever possible.
Finding ways to combat barriers to care – including cultural and socioeconomic barriers – is critical to improving health outcomes. For instance, when working with patients in which you are not able to communicate due to language barriers, you should consider the use of medical translation services to ensure both you and the patient are able to express and receive information adequately. Being inclusive of dietary restrictions and access to food, among many other considerations, impacts the recommendations pharmacists may provide to our patients. However, it is important to remember, we may not be able to ascertain all the information we may deem necessary, so it is important to make the most informed decision (shared between patient and healthcare professional) possible given the information provided.
Related chapters of interest:
- Ethical decision-making in global health: when cultures clash
- More than just diet and exercise: social determinants of health and well-being
- Sex education: counseling patients from various cultural backgrounds
External resources:
- United Nations Sustainable Development Goals. https://sdgs.un.org/
- International Pharmaceutical Federation, Advancing the global pharmaceutical workforce towards achieving universal health coverage and the UN Sustainable Development Goals. https://www.fip.org/www/streamfile.php?filename=fip/PharmacyEducation/2017/WHA_2017.pdf
References
- United Nations. Transforming our world: the 2030 Agenda for Sustainable Development. https://sustainabledevelopment.un.org/post2015/transformingourworld . Accessed December 4, 2020.
- United Nations. The 17 goals. https://sdgs.un.org/goals . Accessed December 4, 2020.


1.6: Voltage and Current in a Practical Circuit
Because it takes energy to force electrons to flow against the opposition of a resistance, there will be voltage manifested (or “dropped”) between any points in a circuit with resistance between them. It is important to note that although the amount of current (the quantity of electrons moving past a given point every second) is uniform in a simple circuit, the amount of voltage (potential energy per unit charge) between different sets of points in a single circuit may vary considerably:
Take this circuit as an example. If we label four points in this circuit with the numbers 1, 2, 3, and 4, we will find that the amount of current conducted through the wire between points 1 and 2 is exactly the same as the amount of current conducted through the lamp (between points 2 and 3). This same quantity of current passes through the wire between points 3 and 4, and through the battery (between points 1 and 4).
However, we will find the voltage appearing between any two of these points to be directly proportional to the resistance within the conductive path between those two points, given that the amount of current along any part of the circuit’s path is the same (which, for this simple circuit, it is). In a normal lamp circuit, the resistance of a lamp will be much greater than the resistance of the connecting wires, so we should expect to see a substantial amount of voltage between points 2 and 3, with very little between points 1 and 2, or between 3 and 4. The voltage between points 1 and 4, of course, will be the full amount of “force” offered by the battery, which will be only slightly greater than the voltage across the lamp (between points 2 and 3).
This, again, is analogous to the water reservoir system:
Between points 2 and 3, where the falling water is releasing energy at the water-wheel, there is a difference of pressure between the two points, reflecting the opposition to the flow of water through the water-wheel. From point 1 to point 2, or from point 3 to point 4, where water is flowing freely through reservoirs with little opposition, there is little or no difference of pressure (no potential energy). However, the rate of water flow in this continuous system is the same everywhere (assuming the water levels in both pond and reservoir are unchanging): through the pump, through the water-wheel, and through all the pipes. So it is with simple electric circuits: the rate of electron flow is the same at every point in the circuit, although voltages may differ between different sets of points.


3.2: Changing Realities
Serves: 4
Cook Time: 5—10 min
Ingredients
- 8—10 Players
- Example of ‘Ask For’: ‘Give me an object’
Instructions
- 4 Players line up
- 1 Player begins with an ‘Ask For’
- Each player subsequently stops the scene and chest it with their own introduction
- The 4th player to enter the scene must find a reason to leave the scene
- After each player leaves the scene it reverts back to the previous moment
- Players may not use dancing as a means of excusing themselves from the scene or beginning one.
Notes
This game begins with a group of 3 to 5 players; though 4 players is ideal. The first player begins the game by making an ‘Ask For’ be it an item, a situation or a profession. At any point the remaining players can call out ‘freeze’, the scene then stops and that player changes the scene to whatever the player(s) appears to look like they are doing. When the final player enters the scene is t is their job to change the location, position, or action of all other players and then find a justifiable reason to leave the scene. After a player leaves the scene all remaining players revert to previous scene but must now justify their new positions or movements. This is repeated until the original player is the only one left on stage.


1.9: Adverbios de frecuencia
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Objetivos
Identify the correct adverb of time for the context
Adverbios de frecuencia
In Spanish, word order may be more flexible than it is in English. These adverbs of time and frequency may be used at the beginning or end of the sentence. However it is more common to see them at the beginning.
To say what someone does before or after another activity, use the expressions “antes de” + infinitive and “después de” + infinitive.
-
Antes de cepillarme los dientes
, yo tomo café.
( Before brushing my teeth, I drink coffee. ) -
Tengo que ducharme
después de hacer ejercicio
.
( I need to shower after exercising. )
Without the preposition “de”, “antes” and “después” change to mean “beforehand” and “afterwards”. They are followed by the conjugated verb.
-
Usualmente hago ejercicio y
después trabajo
.
( Usually I exercise and afterwards I work. ) -
Tengo que hacer mi tarea pero
antes voy a echarme una siesta
.
( I have to do my homework but beforehand, I am going to take a nap. )
To express that you do something once, many times, or a couple of times you use the word “vez” ( time, instance ). Below are a few ways to use this expression, and it comes after the verb or at the end of the sentence.
- Me lavo el pelo tres veces a la semana . ( I wash my hair three times a week. )
- Mi novio se afeita la barba una vez a la semana . ( My boyfriend shaves his beard once a week. )
- Celebramos tu cumpleaños una vez al año . ( We celebrate your birthday once a year. )
“Cada” + a day of the week, month, or another time expression also expresses “every”.


10.7: Torque
- Describe how the magnitude of a torque depends on the magnitude of the lever arm and the angle the force vector makes with the lever arm
- Determine the sign (positive or negative) of a torque using the right-hand rule
- Calculate individual torques about a common axis and sum them to find the net torque
An important quantity for describing the dynamics of a rotating rigid body is torque. We see the application of torque in many ways in our world. We all have an intuition about torque, as when we use a large wrench to unscrew a stubborn bolt. Torque is at work in unseen ways, as when we press on the accelerator in a car, causing the engine to put additional torque on the drive train. Or every time we move our bodies from a standing position, we apply a torque to our limbs. In this section, we define torque and make an argument for the equation for calculating torque for a rigid body with fixed-axis rotation.
Defining Torque
So far we have defined many variables that are rotational equivalents to their translational counterparts. Let’s consider what the counterpart to force must be. Since forces change the translational motion of objects, the rotational counterpart must be related to changing the rotational motion of an object about an axis. We call this rotational counterpart torque .
In everyday life, we rotate objects about an axis all the time, so intuitively we already know much about torque. Consider, for example, how we rotate a door to open it. First, we know that a door opens slowly if we push too close to its hinges; it is more efficient to rotate a door open if we push far from the hinges. Second, we know that we should push perpendicular to the plane of the door; if we push parallel to the plane of the door, we are not able to rotate it. Third, the larger the force, the more effective it is in opening the door; the harder you push, the more rapidly the door opens. The first point implies that the farther the force is applied from the axis of rotation, the greater the angular acceleration; the second implies that the effectiveness depends on the angle at which the force is applied; the third implies that the magnitude of the force must also be part of the equation. Note that for rotation in a plane, torque has two possible directions. Torque is either clockwise or counterclockwise relative to the chosen pivot point. Figure \(\PageIndex{1}\) shows counterclockwise rotations.
Now let’s consider how to define torques in the general three-dimensional case.
When a force \(\vec{F}\) is applied to a point P whose position is \(\vec{r}\) relative to O (Figure \(\PageIndex{2}\)), the torque \(\vec{\tau}\) around O is
\[\vec{\tau} = \vec{r} \times \vec{F} \ldotp \label{10.22}\]
Figure \(\PageIndex{2}\): The torque is perpendicular to the plane defined by \(\vec{r}\) and \(\vec{F}\) and its direction is determined by the right-hand rule.
From the definition of the cross product, the torque \(\vec{\tau}\) is perpendicular to the plane containing \(\vec{r}\) and \(\vec{F}\) and has magnitude
\[|\vec{\tau}| = |\vec{r} \times \vec{F}| = rF \sin \theta,\]
where \(\theta\) is the angle between the vectors \(\vec{r}\) and \(\vec{F}\). The SI unit of torque is newtons times meters, usually written as N • m. The quantity r \(\perp\) = rsin \(\theta\) is the perpendicular distance from O to the line determined by the vector \(\vec{F}\) and is called the lever arm . Note that the greater the lever arm, the greater the magnitude of the torque. In terms of the lever arm, the magnitude of the torque is
\[|\vec{\tau}| = r_{\perp} F \ldotp \label{10.23}\]
The cross product \(\vec{r} \times \vec{F}\) also tells us the sign of the torque. In Figure \(\PageIndex{2}\), the cross product \(\vec{r} \times \vec{F}\) is along the positive z-axis, which by convention is a positive torque. If \(\vec{r} \times \vec{F}\) is along the negative z-axis, this produces a negative torque.
If we consider a disk that is free to rotate about an axis through the center, as shown in Figure \(\PageIndex{3}\), we can see how the angle between the radius \(\vec{r}\) and the force \(\vec{F}\) affects the magnitude of the torque. If the angle is zero, the torque is zero; if the angle is 90°, the torque is maximum. The torque in Figure \(\PageIndex{3}\) is positive because the direction of the torque by the right-hand rule is out of the page along the positive z-axis. The disk rotates counterclockwise due to the torque, in the same direction as a positive angular acceleration.
Any number of torques can be calculated about a given axis. The individual torques add to produce a net torque about the axis. When the appropriate sign (positive or negative) is assigned to the magnitudes of individual torques about a specified axis, the net torque about the axis is the sum of the individual torques:
\[\vec{\tau}_{net} = \sum_{i} |\vec{\tau}_{i}| \ldotp \label{10.24}\]
Calculating Net Torque for Rigid Bodies on a Fixed Axis
In the following examples, we calculate the torque both abstractly and as applied to a rigid body. We first introduce a problem-solving strategy.
- Choose a coordinate system with the pivot point or axis of rotation as the origin of the selected coordinate system.
- Determine the angle between the lever arm \(\vec{r}\) and the force vector.
- Take the cross product of \(\vec{r}\) and \(\vec{F}\) to determine if the torque is positive or negative about the pivot point or axis.
- Evaluate the magnitude of the torque using r \(\perp\) F.
- Assign the appropriate sign, positive or negative, to the magnitude.
- Sum the torques to find the net torque.
Four forces are shown in Figure \(\PageIndex{4}\) at particular locations and orientations with respect to a given xy-coordinate system. Find the torque due to each force about the origin, then use your results to find the net torque about the origin.
Strategy
This problem requires calculating torque. All known quantities––forces with directions and lever arms––are given in the figure. The goal is to find each individual torque and the net torque by summing the individual torques. Be careful to assign the correct sign to each torque by using the cross product of \(\vec{r}\) and the force vector \(\vec{F}\).
Solution
Use |\(\vec{\tau}\)| = r \(\perp\) F = rFsin \(\theta\) to find the magnitude and \(\vec{r} = \vec{r} \times \vec{F}\) to determine the sign of the torque.
The torque from force 40 N in the first quadrant is given by (4)(40)sin 90° = 160 N • m.
The cross product of \(\vec{r}\) and \(\vec{F}\) is out of the page, positive.
The torque from force 20 N in the third quadrant is given by −(3)(20)sin 90° = − 60 N • m.
The cross product of \(\vec{r}\) and \(\vec{F}\) is into the page, so it is negative.
The torque from force 30 N in the third quadrant is given by (5)(30)sin 53° = 120 N • m.
The cross product of \(\vec{r}\) and \(\vec{F}\) is out of the page, positive.
The torque from force 20 N in the second quadrant is given by (1)(20)sin 30° = 10 N • m.
The cross product of \(\vec{r}\) and \(\vec{F}\) is out of the page.
The net torque is therefore \(\tau_{net} = \sum_{i} |\tau_{i}|\) = 160 − 60 + 120 + 10 = 230 N • m.
Significance
Note that each force that acts in the counterclockwise direction has a positive torque, whereas each force that acts in the clockwise direction has a negative torque. The torque is greater when the distance, force, or perpendicular components are greater.
Figure \(\PageIndex{5}\) shows several forces acting at different locations and angles on a flywheel. We have \(|\vec{F}_{1}|\) = 20 N, \(|\vec{F}_{2}|\) = 30 N, \(|\vec{F}_{3}|\) = 30 N, and r = 0.5 m. Find the net torque on the flywheel about an axis through the center.
Strategy
We calculate each torque individually, using the cross product, and determine the sign of the torque. Then we sum the torques to find the net torque. Solution We start with \(\vec{F}_{1}\). If we look at Figure \(\PageIndex{5}\), we see that \(\vec{F}_{1}\) makes an angle of 90° + 60° with the radius vector \(\vec{r}\). Taking the cross product, we see that it is out of the page and so is positive. We also see this from calculating its magnitude:
\[|\vec{\tau}_{1}| = rF_{1} \sin 150^{o} = (0.5\; m)(20\; N)(0.5) = 5.0\; N\; \cdotp m \ldotp\]
Next we look at \(\vec{F}_{2}\). The angle between \(\vec{F}_{2}\) and \(\vec{r}\) is 90° and the cross product is into the page so the torque is negative. Its value is
\[|\vec{\tau}_{2}| = -rF_{2} \sin 90^{o} = (-0.5\; m)(30\; N) = -15.0\; N\; \cdotp m \ldotp\]
When we evaluate the torque due to \(\vec{F}_{3}\), we see that the angle it makes with \(\vec{r}\) is zero so \(\vec{r} \times \vec{F}_{3}\) = 0. Therefore, \(\vec{F}_{3}\) does not produce any torque on the flywheel.
We evaluate the sum of the torques:
\[\tau_{net} = \sum_{i} |\tau_{i}| = 5 - 15 = -10\; N\; \cdotp m \ldotp\]
Significance
The axis of rotation is at the center of mass of the flywheel. Since the flywheel is on a fixed axis, it is not free to translate. If it were on a frictionless surface and not fixed in place, \(\vec{F}_{3}\) would cause the flywheel to translate, as well as \(\vec{F}_{1}\). Its motion would be a combination of translation and rotation.
A large ocean-going ship runs aground near the coastline, similar to the fate of the Costa Concordia , and lies at an angle as shown below. Salvage crews must apply a torque to right the ship in order to float the vessel for transport. A force of 5.0 x 10 5 N acting at point A must be applied to right the ship. What is the torque about the point of contact of the ship with the ground (Figure \(\PageIndex{6}\))?


16.7: Discussion- Managing Globalization
Post 1: Initial Post
Instructions
This posting should be a minimum of one short paragraph and a maximum of two paragraphs. Word totals for this post should be in the 100–200-word range. Whether you agree or disagree, explain why with supporting evidence and concepts from the readings or a related experience. Include a reference, link, or citation when appropriate.
Preparation
As you learned in your reading, globalization is complicated. While it creates new opportunities for businesses and workers, it can also hurt local economies, exploit workers, and threaten the environment. Watch the following video for a crash course on how globalization and free trade affect people living in extreme poverty throughout the world.
For Discussion
Choose ONE of the following questions to respond to in your initial post.
- What responsibility do businesses have to developing economies, workers, and the environment when they choose to pursue global strategies? Do you think corporations like Apple, which has a well-developed global supply chain, have done enough to manage the potential negative effects of their globalized operations?
- When businesses enter global markets, what do you think the role of managers should be in minimizing harm to foreign workers and the environment? Address the planning, organizing, leading, and controlling functions in your response.
- As mentioned in the video, the US produces an annual “List of Goods Produced by Child Labor or Forced Labor.” How effective do you think this is in raising awareness about working conditions in other countries? Do you think pressure from officials, the media, and the public is the best way to prevent companies from doing business with countries that violate international labor standards, or do you think other methods would be more effective?
Posts 2 and 3: Respond to Classmates’ Posts
Instructions
After you have created your initial post, look over the discussion posts of your classmates and give at least two thoughtful responses to two different classmates (one per classmate).
A response posting should be a minimum of one short paragraph. Word totals for these posts should be in the 75–100-word range. Whether you agree or disagree, explain why with supporting evidence and concepts from the readings or a related experience. Include a reference, link, or citation when appropriate. The goal of your response posts is to extend discussions already taking place or pose new possibilities or opinions not previously voiced. Your goal should be to motivate the group discussion and present a creative approach to the topic.
Contributors and Attributions
- Discussion: Managing Globalization. Authored by : Lumen Learning. License : CC BY: Attribution
- General Discussion Instructions. Authored by : Linda Williams and Lumen Learning. Located at : https://courses.lumenlearning.com/wmopen-introbusiness/chapter/discussion-external-factors-internal-pressure/ . License : CC BY: Attribution


28.3C: Mendel’s Model System
The garden pea has several advantageous characteristics that allowed Mendel to develop the laws of modern genetics.
- Describe the scientific reasons for the success of Mendel’s experimental work
Key Points
- Mendel used true-breeding plants in his experiments. These plants, when self-fertilized, always produce offspring with the same phenotype.
- Pea plants are easily manipulated, grow in one season, and can be grown in large quantities; these qualities allowed Mendel to conduct methodical, quantitative analyses using large sample sizes.
- Based on his experiments with the garden peas, Mendel found that one phenotype was always dominant over another recessive phenotype for the same trait.
Key Terms
- phenotype : the observable characteristics of an organism, often resulting from its genetic information or a combination of genetic information and environmental factors
- genotype : the specific genetic information of a cell or organism, usually a description of the allele or alleles relating to a specific gene.
- true-breeding plant : a plant that always produces offspring of the same phenotype when self-fertilized; one that is homozygous for the trait being followed.
Mendel’s Model System
Mendel’s seminal work was accomplished using the garden pea, Pisum sativum , to study inheritance. Pea plant reproduction is easily manipulated; large quantities of garden peas could be cultivated simultaneously, allowing Mendel to conclude that his results did not occur simply by chance. The garden pea also grows to maturity within one season; several generations could be evaluated over a relatively short time.
Pea plants have both male and female parts and can easily be grown in large numbers. For this reason, garden pea plants can either self-pollinate or cross-pollinate with other pea plants. In the absence of outside manipulation, this species naturally self-fertilizes: ova (the eggs) within individual flowers are fertilized by pollen (containing the sperm cell) from the same flower. The sperm and the eggs that produce the next generation of plants both come from the same parent. What’s more, the flower petals remain sealed tightly until after pollination, preventing pollination from other plants. The result is highly inbred, or “true-breeding,” pea plants. These are plants that always produce offspring that look like the parent. Today, we know that these “true-breeding” plants are homozygous for most traits.
A gardener or researcher, such as Mendel, can cross-pollinate these same plants by manually applying sperm from one plant to the pistil (containing the ova) of another plant. Now the sperm and eggs come from different parent plants. When Mendel cross-pollinated a true-breeding plant that only produced yellow peas with a true-breeding plant that only produced green peas, he found that the first generation of offspring is always all yellow peas. The green pea trait did not show up. However, if this first generation of yellow pea plants were allowed to self-pollinate, the following or second generation had a ratio of 3:1 yellow to green peas.
In this and all the other pea plant traits Mendel followed, one form of the trait was “dominant” over another so it masked the presence of the other “recessive” form in the first generation after cross-breeding two homozygous plants.. Even if the phenotype (visible form) is hidden, the genotype (allele controlling that form of the trait) can be passed on to next generation and produce the recessive form in the second generation. By experimenting with true-breeding pea plants, Mendel avoided the appearance of unexpected (recombinant) traits in offspring that might occur if the plants were not true breeding.
Mendel’s Experiments With Peas : Experimenting with thousands of garden peas, Mendel uncovered the fundamentals of genetics.
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7.5: Power
- Relate the work done during a time interval to the power delivered
- Find the power expended by a force acting on a moving body
The concept of work involves force and displacement; the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between two points on its trajectory. None of these quantities or relations involves time explicitly, yet we know that the time available to accomplish a particular amount of work is frequently just as important to us as the amount itself. In the chapter-opening figure, several sprinters may have achieved the same velocity at the finish, and therefore did the same amount of work, but the winner of the race did it in the least amount of time.
We express the relation between work done and the time interval involved in doing it, by introducing the concept of power. Since work can vary as a function of time, we first define average power as the work done during a time interval, divided by the interval,
\[P_{ave} = \frac{\Delta W}{\Delta t} \ldotp \label{7.10}\]
Then, we can define the instantaneous power (frequently referred to as just plain power ).
Power is defined as the rate of doing work, or the limit of the average power for time intervals approaching zero,
\[P = \frac{dW}{dt} \ldotp \label{7.11}\]
If the power is constant over a time interval, the average power for that interval equals the instantaneous power, and the work done by the agent supplying the power is
\[W = P \Delta t.\]
If the power during an interval varies with time (i.e., \(P(t)\)), then the work done is the time integral of the power,
\[W = \int P (t) dt \ldotp\]
The work-energy theorem relates how work can be transformed into kinetic energy. Since there are other forms of energy as well, as we discuss in the next chapter, we can also define power as the rate of transfer of energy. Work and energy are measured in units of joules, so power is measured in units of joules per second, which has been given the SI name watts, abbreviation W: 1 J/s = 1 W. Another common unit for expressing the power capability of everyday devices is horsepower: 1 hp = 746 W.
An 80-kg army trainee does pull-ups on a horizontal bar (Figure \(\PageIndex{1}\)). It takes the trainee 0.8 seconds to raise the body from a lower position to where the chin is above the bar. How much power do the trainee’s muscles supply moving his body from the lower position to where the chin is above the bar? ( Hint : Make reasonable estimates for any quantities needed.)
Strategy
The work done against gravity, going up or down a distance \(\Delta\)y, is mg\(\Delta\)y. Let’s assume that \(\Delta\)y = 2 ft ≈ 60 cm. Also, assume that the arms comprise 10% of the body mass and are not included in the moving mass. With these assumptions, we can calculate the work done.
Solution
The result we get, applying our assumptions, is
\[P=\frac{\operatorname{mg}(\Delta y)}{t}=\frac{0.9(80 \: \mathrm{kg})\left(9.8 \: \mathrm{m} / \mathrm{s}^{2}\right)(0.60 \: \mathrm{m})}{0.8 \: \mathrm{s}}=529 \: \mathrm{W}\]
Significance
This is typical for power expenditure in strenuous exercise; in everyday units, it’s somewhat more than one horsepower (1 hp = 746 W).
Estimate the power expended by a weightlifter raising a 150-kg barbell 2 m in 3 s.
- Answer
-
Add texts here. Do not delete this text first.
The power involved in moving a body can also be expressed in terms of the forces acting on it. If a force \(\vec{F}\) acts on a body that is displaced d\(\vec{r}\) in a time dt, the power expended by the force is
\[P = \frac{dW}{dt} = \frac{\vec{F}\; \cdotp d \vec{r}}{dt} = \vec{F}\; \cdotp \left(\dfrac{d \vec{r}}{dt}\right) = \vec{F}\; \cdotp \vec{v}, \label{7.12}\]
where \(\vec{v}\) is the velocity of the body. The fact that the limits implied by the derivatives exist, for the motion of a real body, justifies the rearrangement of the infinitesimals.
How much power must an automobile engine expend to move a 1200-kg car up a 15% grade at 90 km/h (Figure \(\PageIndex{2}\))? Assume that 25% of this power is dissipated overcoming air resistance and friction.
Strategy
At constant velocity, there is no change in kinetic energy, so the net work done to move the car is zero. Therefore the power supplied by the engine to move the car equals the power expended against gravity and air resistance. By assumption, 75% of the power is supplied against gravity, which equals m\(\vec{g}\; \cdotp \vec{v}\) = mgv sin \(\theta\), where \(\theta\) is the angle of the incline. A 15% grade means tan \(\theta\) = 0.15. This reasoning allows us to solve for the power required.
Solution
Carrying out the suggested steps, we find
\[0.75 P = mgv \sin(\tan^{−1} 0.15),\]
or
\[P = \frac{(1200 \times 9.8\; N)(\frac{90\; m}{3.6\; s}) \sin (8.53^{o})}{0.75} = 58\; kW,\]
or about 78 hp. (You should supply the steps used to convert units.)
Significance
This is a reasonable amount of power for the engine of a small to mid-size car to supply (1 hp = 0.746 kW). Note that this is only the power expended to move the car. Much of the engine’s power goes elsewhere, for example, into waste heat. That’s why cars need radiators. Any remaining power could be used for acceleration, or to operate the car’s accessories.


46.2D: Ecological Pyramids
- Explain the shape and structure of the ecological pyramid
Modeling ecosystems energy flow: ecological pyramids
The structure of ecosystems can be visualized with ecological pyramids, which were first described by the pioneering studies of Charles Elton in the 1920s. Ecological pyramids show the relative amounts of various parameters (such as number of organisms, energy, and biomass) across trophic levels. Ecological pyramids can also be called trophic pyramids or energy pyramids.
Pyramids of numbers can be either upright or inverted, depending on the ecosystem. A typical grassland during the summer has an upright shape since it has a base of many plants, with the numbers of organisms decreasing at each trophic level. However, during the summer in a temperate forest, the base of the pyramid consists of few trees compared with the number of primary consumers, mostly insects. Because trees are large, they have great photosynthetic capability and dominate other plants in this ecosystem to obtain sunlight. Even in smaller numbers, primary producers in forests are still capable of supporting other trophic levels.
Another way to visualize ecosystem structure is with pyramids of biomass. This pyramid measures the amount of energy converted into living tissue at the different trophic levels. Using the Silver Springs ecosystem example, this data exhibits an upright biomass pyramid, whereas the pyramid from the English Channel example is inverted. The plants (primary producers) of the Silver Springs ecosystem make up a large percentage of the biomass found there. However, the phytoplankton in the English Channel example make up less biomass than the primary consumers, the zooplankton. As with inverted pyramids of numbers, the inverted biomass pyramid is not due to a lack of productivity from the primary producers, but results from the high turnover rate of the phytoplankton. The phytoplankton are consumed rapidly by the primary consumers, which minimizes their biomass at any particular point in time. However, since phytoplankton reproduce quickly, they are able to support the rest of the ecosystem.
Pyramid ecosystem modeling can also be used to show energy flow through the trophic levels. Pyramids of energy are always upright, since energy is lost at each trophic level; an ecosystem without sufficient primary productivity cannot be supported. All types of ecological pyramids are useful for characterizing ecosystem structure. However, in the study of energy flow through the ecosystem, pyramids of energy are the most consistent and representative models of ecosystem structure.
Key Points
- Pyramids of numbers can be either upright or inverted, depending on the ecosystem.
- Pyramids of biomass measure the amount of energy converted into living tissue at the different trophic levels.
- The English Channel ecosystem exhibits an inverted biomass pyramid since the primary producers make up less biomass than the primary consumers.
- Pyramid ecosystem modeling can also be used to show energy flow through the trophic levels; pyramids of energy are always upright since energy decreases at each trophic level.
- All types of ecological pyramids are useful for characterizing ecosystem structure; however, in the study of energy flow through the ecosystem, pyramids of energy are the most consistent and representative models of ecosystem structure.
Key Terms
- ecological pyramid : diagram that shows the relative amounts of energy or matter or numbers of organisms within each trophic level in a food chain or food web


7.9: Summary of Key Concepts
Summary of Key Concepts
Graph of a Function
The geometric representation (picture) of the solutions to an equation is called the graph of the equation.
Axis
An axis is the most basic structure of a graph. In mathematics, the number line is used as an axis.
Number of Variables and the Number of Axes
| An equation in one variable requires one axis | One-dimension |
| An equation in two variables requires two axes. | Two-dimensions |
| An equation in three variables requires three axes. | Three-dimensions. |
| An equation in \(n\) variables requires \(n\) axes | \(n\)-dimensions. |
Coordinate System
A system of axes that is constructed for graphing an equation is called a coordinate system .
Graphing an Equation
The phrase graphing an equation is interpreted as meaning geometrically locating the solutions to that equation.
Uses of a Graph
A graph may reveal information that may not be evident from the equation.
Rectangular Coordinate System \(xy\)-Plane
A rectangular coordinate system is constructed by placing two number lines at 90∘ angles. These lines form a plane that is referred to as the \(xy\)-plane.
Ordered Pairs and Points
For each ordered pair \((a,b)\), there exists a unique point in the plane, and for each point in the plane we can associate a unique ordered pair \((a,b)\) of real numbers.
Graphs of Linear Equations
When graphed, a linear equation produces a straight line.
General Form of a Linear Equation in Two Variables
The general form of a linear equation in two variables is \(ax+by=c\), where \(a\) and \(b\) are not both \(0\).
Graphs, Ordered Pairs, Solutions, and Lines
The graphing of all ordered pairs that solve a linear equation in two variables produces a straight line.
The graph of a linear equation in two variables is a straight line.
If an ordered pair is a solution to a linear equation in two variables, then it lies on the graph of the equation.
Any point (ordered pair) that lies on the graph of a linear equation in two variables is a solution to that equation.
Intercept
An intercept is a point where a line intercepts a coordinate axis.
Intercept Method
The intercept method is a method of graphing a linear equation in two variables by finding the intercepts, that is, by finding the points where the line crosses the \(x\)-axis and the \(y\)-axis.
Slanted, Vertical, and Horizontal Lines
An equation in which both variables appear will graph as a
slanted
line.
A linear equation in which only one variable appears will graph as either a
vertical
or
horizontal
line.
\(x=a\) graphs as a vertical line passing through \(a\) on the \(x\)-axis.
\(y=b\) graphs as a horizontal line passing through \(b\) on the \(y\)-axis.
Slope of a Line
The slope of a line is a measure of the line’s steepness. If \((x_1,y_1)\) and \((x_2,y_2)\) are any two points on a line, the slope of the line passing through these points can be found using the slope formula.
\(m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{\text{ vertical change }}{\text{ horizontal change }}\)
Slope and Rise and Decline
Moving left to right, lines with positive slope rise, and lines with negative slope decline.
Graphing an Equation Given in Slope-Intercept Form
An equation written in slope-intercept form can be graphed by
- Plotting the \(y\)-intercept \((0,b)\).
- Determining another point using the slope, \(m\).
- Drawing a line through these two points.
Forms of Equations of Lines
General Form: \(ax + by + c\)
Slope-Intercept Form: \(y = mx + b\)
To use this form, the slope and \(y\)-intercept are needed
Point-Slope Form: \(y - y_1 = m(x - x_1)\)
To use this form, the slope and one points, or two points, are needed.
Half-Planes and Boundary Lines
A straight line drawn through the plane divides the plane into two half-planes . The straight line is called a boundary line .
Solution to an Inequality in Two Variables
A solution to an inequality in two variables is a pair of values that produce a true statement when substituted into the inequality.
Location of Solutions to Inequalities in Two Variables
All solutions to a linear inequality in two variables are located in one, and only one, half-plane.


15.8: Spectroscopy of Aromatic Compounds
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Objectives
After completing this section, you should be able to
- determine whether an unknown compound contains an aromatic ring by inspection of its infrared spectrum, given a table of characteristic infrared absorptions.
- state the approximate chemical shift of aryl protons in a proton NMR spectrum.
- explain why signals resulting from the presence of aryl protons are found downfield from those caused by vinylic protons in a proton NMR spectrum.
- propose possible structures for an unknown aromatic compound, given its proton NMR spectrum, other spectroscopic data (such as a 13 C NMR or infrared spectrum), or both.
Key Terms
Make certain that you can define, and use in context, the key term below.
- ring current
Study Notes
It is not necessary that you memorize detailed spectroscopic data. In the laboratory, on assignments and when writing examinations, you will be provided with a table of characteristic infrared absorptions to assist you in interpreting infrared spectra.
The important points to note about the proton NMR of aromatic compounds are the approximate chemical shifts of such protons and the complex splitting pattern that is sometimes observed. You are advised not to spend too long trying to understand why the signal for an aryl proton is found downfield from the signal for a vinylic proton. In general, we want you to be able to interpret NMR spectra, and leave the underlying theory for subsequent chemistry courses.
The chemical shifts of aromatic protons
Some protons resonate much further downfield than can be accounted for simply by the deshielding effect of nearby electronegative atoms. Vinylic protons (those directly bonded to an alkene carbon) and aromatic (benzylic) protons are dramatic examples.
We'll consider the aromatic proton first. Recall that in benzene and many other aromatic structures, a sextet of p electrons is delocalized around the ring. When the molecule is exposed to B 0 , these p electrons begin to circulate in a ring current , generating their own induced magnetic field that opposes B 0 . In this case, however, the induced field of the p electrons does not shield the benzylic protons from B 0 as you might expect– rather, it causes the protons to experience a stronger magnetic field in the direction of B 0 – in other words, it adds to B 0 rather than subtracting from it.
To understand how this happens, we need to understand the concept of diamagnetic anisotropy (anisotropy means `non-uniformity`). So far, we have been picturing magnetic fields as being oriented in a uniform direction. This is only true over a small area. If we step back and take a wider view, however, we see that the lines of force in a magnetic field are actually anisotropic. They start in the 'north' direction, then loop around like a snake biting its own tail.
If we are outside the ring in the figure above, we feel a magnetic field pointing in a northerly direction. If we are inside the ring, however, we feel a field pointing to the south.
In the induced field generated by the aromatic ring current, the benzylic protons are outside the ring – this means that the induced current in this region of space is oriented in the same direction as B 0 .
In total, the benzylic protons are subjected to three magnetic fields: the applied field (B 0 ) and the induced field from the electrons pointing in one direction, and the induced field of the non-aromatic electrons pointing in the opposite (shielding) direction. The end result is that benzylic protons, due to the anisotropy of the induced field generated by the ring current, appear to be highly de-shielded. Their chemical shift is far downfield, in the 6.5-8 ppm region.
The presence of anisotropy effects is often used to indicate aromaticity in a molecule. An example is the nonaromatic 8 pi electron cyclooctatetraene. In order to avoid anti-aromatic destabilization, the molecule takes a non-planar conformation which prevents conjugation and ring currents. Consequently, the molecule's protons absorbed at 5.8 ppm which is within the alkene region of 1 H NMR.
Exercise \(\PageIndex{1}\)
The 1 H-NMR spectrum of [18] annulene has two peaks, at 8.9 ppm and -1.8 ppm (upfield of TMS!) with an integration ratio of 2:1. Explain the unusual chemical shift of the latter peak.
- Answer
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The molecule contains two groups of equivalent protons: the twelve pointing to the outside of the ring, and the six pointing into the center of the ring. The molecule is aromatic, as evidenced by the chemical shift of the ‘outside’ protons’ (and the fact that there are 18 p electrons - a Hückel number). The inside protons are shielded by the induced field of the aromatic ring current, because inside the ring this field points in the opposite direction of B 0 . This is the source of the unusually low (negative relative to TMS) chemical shift for these protons.
Characteristic 1 H NMR Absorptions of Aromatic Compounds
Protons directly attached to an aromatic ring, commonly called aryl protons, show up about 6.5-8.0 PPM. This range is typically called the aromatic region of an 1 H NMR spectrum. Protons on carbons directly bonded to an aromatic ring, called benzylic protons, show up about 2.0-3.0 PPM.
'
For the 1 H NMR spectrum of p-bromotoluene, the absorption for the benzylic protons appears as a strong singlet at 2.28 ppm. Due to the molecule's symmetry, the aryl protons appear as two doublets at 6.96 & 7.29 ppm.
Characteristic 13 C NMR Absorptions of Aromatic Compounds
Carbons in an aromatic ring absorb in the range of 120-150 ppm in a 13 C NMR spectrum. This is virtually the same range as nonaromatic alkenes (110-150 ppm) so peaks in this region are not definitive proof of a molecule's aromaticity.
Due to the decoupling in 13 C NMR, the number of absorptions due to aromatic carbons can easily be observed. This can be used to determine the relative positions ( ortho , meta , or para ) for di-substituted benzenes. Peak assignments can be simplified by noting that 13 C peaks tend to be larger if two carbons contribute to the absorption.
Symmetrical Di-substituted Benzenes
Benzenes substituted with two identical groups have a relatively high amount of symmetry. In all three configurations, there is a plane of symmetry which reduces the number of distinct aryl carbon absorptions to less than six. The ortho configuration has a plane of symmetry which mirrors each carbon in the benzene ring causing only three 13 C aryl absorptions to occur. The meta configuration's plane of symmetry mirrors two carbons of the benzene ring allowing for four aryl absorptions to occur. The para configuration actually has two planes of symmetry (one vertical and one horizontal on the structure below) through the benzene ring, which only allows two distinct aryl absorptions to occur.
Asymmetrical Di-substituted Benzenes
The lack of a plane of symmetry in asymmetrical di-substituted benzenes makes each carbon in the ortho and meta configuration unique. Consequently, their 13 C NMR spectra show six arene absorptions. However, the para configuration has a plane of symmetry drawn through the two substituents which mirrors two carbons of the benzene ring causing only 4 arene absorptions to appear.
Example \(\PageIndex{1}\)
Charateristic IR Absorption of Benzene Derivatives
Arenes have absorption bands in the 650-900 cm −1 region due to bending of the C–H bond out of the plane of the ring. The exact placement of these absorptions can indicate the pattern of substitution on a benzene ring. However, this is beyond the scope of introductory organic chemistry. Arenes also possess a characteristic absorption at about 3030-3100 cm −1 as a result of the aromatic C–H stretch. It is somewhat higher than the alkyl C–H stretch (2850–2960 cm −1 ), but falls in the same region as olefinic compounds. Two bands (1500 and 1660 cm −1 ) caused by C=C in plane vibrations are the most useful for characterization as they are intense and are likely observed.
In aromatic compounds, each band in the spectrum can be assigned:
- C–H stretch from 3100-3000 cm -1
- overtones, weak, from 2000-1665 cm -1
- C–C stretch (in-ring) from 1600-1585 cm -1
- C–C stretch (in-ring) from 1500-1400 cm -1
- C–H "oop" from 900-675 cm -1
Note that this is at slightly higher frequency than is the –C–H stretch in alkanes. This is a very useful tool for interpreting IR spectra. Only alkenes and aromatics show a C–H stretch slightly higher than 3000 cm -1 .
Ultraviolet Spectroscopy
The presence of conjugated π bonds makes aromatic rings detectable in a UV/Vis spectrum. Benzene primarily absorbs through a be a π-π* transition over the range from 160-208 nm wi th a λ max v alue of about 178 nm.
Benzene shows a less intense absorption in 230-276 nm range. These absorptions are due to vibrational fine structure often displayed by rigid molecules such as benzene and other aromatic compounds.


18.1: Introduction to Blood Vessels and Circulation
Chapter Learning Objectives:
After studying this chapter, you will be able to:
- Compare and contrast the anatomical structure of arteries, arterioles, capillaries, venules, and veins
- Describe how blood flow, blood pressure, and resistance interrelate
- Describe the interaction of the cardiovascular system with other body systems
- Label the major blood vessels of the pulmonary and systemic circulations
- Identify and describe the hepatic portal system
- Describe the development of blood vessels and fetal circulation
- Compare fetal circulation to that of an individual after birth
In this chapter, you will learn about the vascular part of the cardiovascular system, that is, the vessels that transport blood throughout the body and provide the physical site where gases, nutrients, and other substances are exchanged with body cells. When vessel functioning is reduced, blood-borne substances do not circulate effectively throughout the body. As a result, tissue injury occurs, metabolism is impaired, and the functions of every body system are threatened.
Contributors and Attributions
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OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


2.1: Predicates and Logical Connectives
In every branch of Mathematics there are special, atomic, notions that defy precise definition. In Geometry, for example, the atomic notions are points, lines and their incidence. Euclid defines a point as “that which has no part” – people can argue (and have argued) incessantly over what exactly is meant by this. Is it essentially saying that anything without volume, area or length of some sort is a point? In modern times it has been recognized that any formal system of argumentation has to have such elemental, undefined, concepts – and that Euclid’s apparent lapse in precision comes from an attempt to hide this basic fact. The notion of “point” can’t really be defined. All we can do is point (no joke intended) at a variety of points and hope that our audience will absorb the same concept of point that we hold via the process of induction 1 .
The atomic concepts in Set Theory are “set”, “element” and “membership”. The atomic concepts in Logic are “true”, “false”, “sentence” and “statement”.
Regarding true and false , we hope there is no uncertainty as to their meanings. Sentence also has a well-understood meaning that most will agree on – a syntactically correct ordered collection of words such as “Johnny was a football player.” or “Red is a color.” or “This is a sentence which does not refer to itself.” A statement is a sentence which is either true or false. In other words, a statement is a sentence whose truth value is definite , in more other words, it is always possible to decide – one way or the other – whether a statement is true or false. 2 The first example of a sentence given above (“Johnny was a football player”) is not a statement – the problem is that it is ambiguous unless we know who Johnny is. If it had said “Johnny Unitas was a football player.” then it would have been a statement. If it had said “Johnny Appleseed was a football player.” it would also have been a statement, just not a true one.
Ambiguity is only one reason that a sentence may not be a statement. As we consider more complex sentences, it may be the case that the truth value of a given sentence simply cannot be decided. One of the most celebrated mathematical results of the \(20^{\text{th}}\) century is Kurt Gödel’s “Incompleteness Theorem.” An important aspect of this theory is the proof that in any axiomatic system of mathematical thought there must be undecidable sentences – statements which can neither be proved nor disproved from the axioms 3 . Simple sentences (e.g. those of the form subject-verb-object) have little chance of being undecidable for this reason, so we will next look at ways of building more complex sentences from simple components.
Let’s start with an example. Suppose I come up to you in some windowless room and make the statement: “The sun is shining but it’s raining!” You decide to investigate my claim and determine its veracity. Upon reaching a room that has a view of the exterior there are four possible combinations of sunniness and/or precipitation that you may find. That is, the atomic predicates “The sun is shining” and “It is raining” can each be true or false independently of one another. In the following table we introduce a convention used throughout the remainder of this book – that true is indicated with a capital letter \(\text{T}\) and false is indicated with the Greek letter \(\phi\) (which is basically a Greek \(\text{F}\), and is a lot harder to mistake for a \(\text{T}\) than an \(\text{F}\) is.)
| The Sun is Shining | It is Raining |
|---|---|
| \(\text{T}\) | \(\text{T}\) |
| \(\text{T}\) | \(\phi\) |
| \(\phi\) | \(\text{T}\) |
| \(\phi\) | \(\phi\) |
Each row of the above table represents a possible state of the outside world. Suppose you observe the conditions given in the last row, namely that it is neither sunny, nor is it raining – you would certainly conclude that I am not to be trusted. I.e. my statement, the compounding of “The sun is shining” and “It is raining” (with the word “but” in between as a connector) is false. If you think about it a bit, you’ll agree that this so-called compound sentence is true only in the case that both of its component pieces are true. This underscores an amusing linguistic point: “but” and “and” have exactly the same meaning! More precisely, they denote the same thing, they have subtly different connotations however – “but” indicates that both of the statements it connects are true and that the speaker is surprised by this state of affairs.
In Mathematics we distinguish two main connectives for hooking-up simple sentences into compound ones. The conjunction of two sentences is the compound sentence made by sticking the word “and” between them. The disjunction of two sentences is formed by placing an “or” between them. Conjunctions are true only when both components are true. Disjunctions are false only when both components are false.
As usual, mathematicians have developed an incredibly terse, compact notation for these ideas. 4 First, we represent an entire sentence by a single letter – traditionally, a capital letter. This is called a predicate variable. For example, following the example above, we could denote the sentence “The sun is shining” by the letter \(\text{S}\). Similarly, we could make the assignment \(\text{R} =\) “It is raining.” The conjunction and disjunction of these sentences can then be represented using the symbols \(S ∧ R and \(S ∨ R\), respectively. As a mnemonic, note that the connective in \(S ∧ R\) looks very much like the capital letter \(\text{A}\) (as in And).
To display, very succinctly, the effect of these two connectives we can use so-called truth tables. In a truth table, we list all possible truth values of the predicate variables and then enumerate the truth values of some compound sentence. For the conjunction and disjunction connectors we have (respectively):
| \(A\) | \(B\) | \(A ∧ B\) |
|---|---|---|
| \(\text{T}\) | \(\text{T}\) | \(\text{T}\) |
| \(\text{T}\) | \(\phi\) | \(\phi\) |
| \(\phi\) | \(\text{T}\) | \(\phi\) |
| \(\phi\) | \(\phi\) | \(\phi\) |
and
| \(A\) | \(B\) | \(A ∨ B\) |
|---|---|---|
| \(\text{T}\) | \(\text{T}\) | \(\text{T}\) |
| \(\text{T}\) | \(\phi\) | \(\text{T}\) |
| \(\phi\) | \(\text{T}\) | \(\text{T}\) |
| \(\phi\) | \(\phi\) | \(\phi\) |
In addition to these connectors we need a modifier (called negation) that acts on individual sentences. The negation of a sentence \(A\) is denoted by \(¬A\), and its truth value is exactly the opposite of \(A\)’s truth value. The negation of a sentence is also known as the denial of a sentence. A truth table for the negation operator is somewhat trivial but we include it here for completeness.
| \(A\) | \(¬A\) |
|---|---|
| \(\text{T}\) | \(\phi\) |
| \(\phi\) | \(\text{T}\) |
These three simple tools (and, or & not) are sufficient to create extraordinarily complex sentences out of basic components. The way these pieces interrelate is a bit reminiscent of algebra, in fact, the study of these logical operators (or any operators that act like them) is called Boolean Algebra 5 . There are distinct differences between Boolean and ordinary algebra however. In regular algebra we have the binary connectors \(+\) (plus) and \(·\) (times), and the unary negation operator \(−\), these are certainly analogous to \(∧\), \(∨\) & \(¬\), but there are certain consequences of the fact that multiplication is effectively repeated addition that simply don’t hold for the Boolean operators. For example, there is a well-defined precedence between \(·\) and \(+\). In parsing the expression \(4 · 5 + 3\) we all know that the multiplication is to be done first. There is no such rule governing order of operations between \(∧\) and \(∨\), so an expression like \(A ∧ B ∨ C\) is simply ambiguous – it must have parentheses inserted in order to show the order, either \((A∧B)∨C\) or \(A∧(B∨C)\). Another distinction between ordinary and Boolean algebra is exponentiation. If there were exponents in Boolean algebra, we’d need two different kinds – one for repeated conjunction and another for repeated disjunction.
Why is it that there is no such thing as exponentiation in the algebra of Logic?
While there are many differences between Boolean algebra and the usual, garden-variety algebra, there are also many similarities. For instance, the associative, commutative and distributive laws of Algebra all have versions that work in the Boolean case.
A very handy way of visualizing Boolean expressions is given by digital logic circuit diagrams. To discuss these diagrams we must make a brief digression into Electronics. One of the most basic components inside an electronic device is a transistor, this is a component that acts like a switch for electricity, but the switch itself is controlled by electricity. In Figure \(2.1.1\) we see the usual schematic representation of a transistor. If voltage is applied to the wire labeled \(\text{z}\), the transistor becomes conductive, and current may flow from \(\text{x}\) to \(\text{y}\).
Suppose that two transistors are connected as in Figure \(2.1.2\) (this is called a series connection). In order for current to flow from \(\text{x}\) to \(\text{y}\) we must have voltage applied to both the wires labeled \(\text{z}\) and \(\text{w}\). In other words, this circuit effectively creates the and operation – assuming voltage is always applied to \(\text{x}\), if \(z\) and \(\text{w}\) are energized then the output at \(\text{y}\) will be energized.
When two transistors are connected in parallel (this is illustrated in Figure \(2.1.3\)) current can flow from \(\text{x}\) to \(\text{y}\) when either (or both ) of the wires at \(\text{z}\) and \(\text{w}\) have voltage applied. This brings up a point which is confusing for some: in common speech the use of the word “or” often has the sense known as exclusive or (a.k.a. xor), when we say “\(\text{X}\) or \(\text{Y}\)” we mean “Either X or Y, but not both.” In Electronics and Mathematics, or always has the non-exclusive (better known as inclusive) sense.
As a sort of graphical shorthand, electronics engineers use the symbols below to indicate and-gates, or-gates & not-gates (better known as negators).
An and-gate has two transistors inside it that are wired in series – if both the inputs are energized the output will be too. An or-gate has two transistors in parallel inside it. Not-gates involve magic – when their input is not on, their output is and vice versa.
Using this graphical “language” one can make schematic representations of logical expressions. Some find that tracing such diagrams makes understanding the structure of a Boolean expression easier. For example, in Figure \(2.1.4\) we illustrate \(2\) of the possible ways that the conjunction of four predicate variables can be parenthesized. In fact, when a multitude of predicates are joined by the same connective, the way in which the expression is parenthesized is unimportant, thus one often sees a further shorthand — gates with more than \(2\) inputs.
A common task for an electronics designer is to come up with a digital logic circuit having a prescribed input/output table. Note that an input/output table for a logic circuit is entirely analogous with a truth table for a compound sentence in Logic — except that we use \(0\)’s and \(1\)’s rather than \(\text{T}\)’s and \(\phi\)’s.
Suppose that we wanted to design a circuit that would have the following input/output table.
| \(x\) | \(y\) | \(z\) | \(\text{out}\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(0\) | \(1\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(0\) |
| \(1\) | \(0\) | \(1\) | \(0\) |
| \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) |
A systematic method for accomplishing such a design task involves a notion called disjunctive normal form . A Boolean expression is in disjunctive normal form if it consists of the disjunction of one or more statements, each of which consists entirely of conjunctions of predicate variables and/or their negations. In other words, the or of a bunch of ands . In terms of digital logic circuits, the ands we’re talking about are called recognizers . For example, the following \(3\)-input and-gates recognize the input states in the \(4^{\text{th}}\), \(7^{\text{th}}\) and \(8^{\text{th}}\) rows of the i/o table above. (These are the rows where the output is supposed to be \(1\).)
In Figure \(2.1.5\) we illustrate how to create a circuit whose i/o table is as above using these recognizers.
Exercises
Design a digital logic circuit (using and, or & not gates) that implements an exclusive or
Consider the sentence “This is a sentence which does not refer to itself.” which was given in the beginning of this chapter as an example. Is this sentence a statement? If so, what is its truth value?
Consider the sentence “This sentence is false.” Is this sentence a statement?
Complete truth tables for each of the sentences \((A∧B)∨C\) and \(A∧(B∨ C)\). Does it seem that these sentences have the same logical content?
There are two other logical connectives that are used somewhat less commonly than \(∨\) and \(∧\). These are the Scheffer stroke and the Peirce arrow – written \(|\) and \(↓\), respectively — they are also known as NAND and NOR.
The truth tables for these connectives are:
| \(A\) | \(B\) | \(A|B\) |
|---|---|---|
| \(\text{T}\) | \(\text{T}\) | \(\phi\) |
| \(\text{T}\) | \(\phi\) | \(\text{T}\) |
| \(\phi\) | \(\text{T}\) | \(\text{T}\) |
| \(\phi\) | \(\phi\) | \(\text{T}\) |
and
| \(A\) | \(B\) | \(A↓B\) |
|---|---|---|
| \(\text{T}\) | \(\text{T}\) | \(\phi\) |
| \(\text{T}\) | \(\phi\) | \(\phi\) |
| \(\phi\) | \(\text{T}\) | \(\phi\) |
| \(\phi\) | \(\phi\) | \(\text{T}\) |
Find an expression for \((A ∧ ¬B) ∨ C\) using only these new connectives (as well as negation and the variable symbols themselves)
The famous logician Raymond Smullyan devised a family of logical puzzles around a fictitious place he called “the Island of Knights and Knaves.” The inhabitants of the island are either knaves, who always make false statements, or knights, who always make truthful statements.
In the most famous knight/knave puzzle, you are in a room which has only two exits. One leads to certain death and the other to freedom. There are two individuals in the room, and you know that one of them is a knight and the other is a knave, but you don’t know which. Your challenge is to determine the door which leads to freedom by asking a single question.


44: So, What Really Is Jihad? (Khalil)
Mohammad Hassan Khalil
#civilrights #politics #religion #currentevents #global #definition
This term ‘jihad’ can include various forms of nonviolent struggles: for instance, the struggle to become a better person. "Studying in the Mosque" by tjulrich is licensed under CC BY-NC-SA 4.0 / A derivative from the original work (cropped)
Often, many people conflate the terms jihad and terrorism. This is in part because many writers use the term “jihadist” when describing violent Muslim radicals.
To be sure, such radicals have invoked jihad to justify their heinous acts, such as the 9/11 attacks on the World Trade Center and more recent Islamic State group (also known as ISIS) operations . But these acts have been strongly condemned by numerous Muslim clerics and scholars on Islamic grounds.
And as I show in my own research , violent radicals who attempt to justify terrorism on religious grounds are often misrepresenting the scholarly sources they cite.
Jihad, according to Islamic law
The Arabic term jihad literally means a “struggle” or “striving.” This term appears in the Quran in different contexts and can include various forms of nonviolent struggles: for instance, the struggle to become a better person. This falls under the category of “jihad of the self,” an important subject in Islamic devotional works .
In the specific context of Islamic law, however, jihad generally signifies an armed struggle against outsiders.
Medieval scholars of Islamic law delineated two basic forms of armed jihad: defensive jihad, an armed struggle against invaders; and aggressive jihad, a preemptive or offensive attack commissioned by a political authority.
Not surprisingly, Muslim scholars have long debated when exactly warfare can be justified .
Much less controversial, however, is the general rule that various categories of civilians must not be targeted .
This rule of civilian immunity is so widely accepted that it is even typically recognized by violent Muslim radicals . But such radicals also invoke loopholes to get around this rule. When attempting to justify 9/11, for instance, Osama bin Laden argued, among other things, that American civilians could be targeted since, he asserted, American forces had previously targeted Muslim civilians .
To justify this loophole, bin Laden invoked the writings of medieval Muslim scholars such as al-Qurtubi. As I show in a recent book , however, al-Qurtubi actually held the exact opposite view: Civilians should never be targeted as a form of retribution.
This is but one example of why it is critical not to conflate the prevailing interpretations of jihad with Muslim terrorism.
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Mohammad Hassan Khalil is an associate professor of Religious Studies, an adjunct professor of Law, and Director of the Muslim Studies Program at Michigan State University. He is the is author of Islam and the Fate of Others: The Salvation Question . His essay appeared in The Conversation.
So, what really is jihad by
Mohammad Hassan Khalil
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