1.7: Exercises
- Page ID
- 21955
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. For the following hypothetical situation, state what decision you recommend and why you recommend it. Weigh the pros and cons, and describe your process of weighing the pros and cons.
A West Virginia radio telescope recently detected an unusual signal beamed in our direction from somewhere across the Milky Way galaxy. After six months of study by the world's best scientists, it is agreed that the signal comes from an intelligent source and contains the message which says, when translated into English, "Can you hear us? Describe yourself and where you are located." The continuously repeating message also includes a very brief description of the other civilization, indicating that they are a hydrocarbon-based life form that lives on two planets around a central star. Their signal gave no indication they know we exist. You, a leading government official, have been asked by your president for your opinion about how or whether Earth should respond to the message.1
2. During the rest of the school term, create a journal of pieces of reasoning. Collect examples of reasoning that you find in your own experience. Sources might be web pages, newspaper or TV ads, magazine articles, conversations, books, and so on. Cut out, photocopy, or write up each example on a regular-size page (8.5 x 11 inches). Below each example (or on an accompanying page) identify where the reasoning came from, including page number and the date of publication or broadcast or conversation you heard. Then identify the reasoning that occurs, and defend your identification. Your goal should be fifteen examples. Staple your fifteen pages together in the upper left corner, adding a cover page containing your name and class hour. The best journals will be those that contain a wide variety of examples of ideas from this chapter and future chapters, such as (a) examples of deceptive techniques by advertisers, salespersons, and propagandists, (b) examples of reasoning errors discussed in later chapters, (c) examples of violations of several principles of good reasoning or good criticism, and (d) two to four examples of good reasoning.
3. Columbus Day is an American holiday. Write a short essay that weighs the pros and cons and then comes to a decision about whether there should be more or less public celebration (by Americans and their institutions) on Columbus Day, October 12. Here is some relevant background information to reduce your research time. Christopher Columbus was a brave explorer, an adventurer, a breaker of new ground. Unlike Leif Ericson of Norway and other explorers who also visited the Western Hemisphere before Columbus, Columbus was the principal European who caused large numbers of other Europeans to follow him to the hemisphere. He was integral in causing the Western hemisphere to now have its long history of European culture. He brought new technology and new religion that spread throughout the hemisphere. He sent attack dogs to maul naked Indians, seized Caribbean women as sex slaves, and disemboweled other natives who resisted conquest. Many were hanged, some were burned alive. He chopped off the hands of thousands who were slow in producing the gold he wanted. Many Arawak Indians responded by committing a series of mass suicides. He shipped 500 Arawak Indians back on Europe as slaves, although 200 died on the voyage. He brought Western diseases which spread across North and South America, almost depopulating what is now California. He helped convince many people that the Earth is round. He brought new American foods to Europe and introduced European foods to the Americas. Thanks to Columbus, the wheel and the domesticated horse entered the Americas.
4. Produce three summaries of the Declaration of Independence of the United States. Summary 1 should be 10 to 13 words. Summary 2 should be 30 to 35 words. Summary 3 should be 100-111 words. After each summary, state its word count. Your goal is to successfully communicate the contents of the Declaration, given the word limitations. In doing this, mentally put yourself in the shoes of someone whose only knowledge of what is in the Declaration will come from reading just one of your summaries. The total word count of the Declaration is 1,337 words, not counting signatures.
5. Assume the quotation contains a sensible argument with a word or phrase taken out and replaced with a blank. Choose the best way to fill in the blank. "Juan’s envelope has got to be here somewhere _____ I had it when I left class, I had it when I ate lunch after class, I had it when I was getting in the car to drive here, and I know I didn't drop it until I got in here. The envelope is a mystery, but it can’t just disappear, can it?"2
a. but suppose
b. therefore
c. because
d. but it’s not the case that
e. and
6. Select some decision you made this week and write a short essay (under two pages, typed double-spaced) in which you explicitly weigh the pros and cons of making the choice you made as opposed to alternative choices you might have made.
7. Weigh the pros and cons of whether to sign up for an Internet version of a college course in Asian history instead of the regular version in which you sit in a classroom in front of the instructor. Assume the course tuition is the same either way.
8. Consider Emilio’s reason for drinking the untreated stream water: “Look, if the stream were poisonous, everything in it would look dead. There are water spiders and plants living in the stream. It’s no death trap.” Which statement below best demonstrates the weakness of Emilio’s argument in favor of drinking the water?
a. In arguments, some statements are true; some are false. You cannot always tell which.
b. Some things that will kill water spiders won’t kill the plants, and vice versa.
c. Many things that are harmful to humans are not harmful to water spiders.
d. Before making a decision, one should weigh the pros and cons, yet Emilio isn’t considering the pro side of his own position, namely that water spiders and plants need water, too.
9. In weighing the pros and cons of the camping situation with Emilio and Juanita, you considered whether to pack up and go home, stay and boil the water, or hike for help. If you failed to notice that Juanita had hiked in with a cell phone which you could use to call for information about Giardia, then you would have failed to
a. consider all the possible courses of action.
b. identify the consequences of a course of action.
c. evaluate the consequences of the action.
d. consider the probability that the consequences will occur.
10. In weighing the pros and cons of the camping situation with Emilio and Juanita, you considered whether to pack up and go home, stay and boil the water, or hike for help. If you failed to notice that if you stayed and boiled the water, then you couldn’t drink it right away but would have to wait until it cooled, then you would have failed to
a. consider all the possible courses of action.
b. identify the consequences of the course of action.
c. evaluate the consequences of the course of action.
d. consider the probability that the consequences will occur.
11. In weighing the pros and cons of the camping situation with Emilio and Juanita, you considered whether to pack up and go home, stay and boil the water, or hike for help. You briefly noticed that, if you stayed, then you might all become sick. However, suppose you failed to notice how bad this would be. For example, you might need medical treatment but be too sick to go for help. So, in weighing the pros and cons, you failed to
a. consider all the possible courses of action.
b. identify the consequences of the course of action.
c. evaluate the consequences of the course of action.
d. consider the probability that the consequences will occur.
12. In weighing the pros and cons of the camping situation with Emilio and Juanita, you considered whether to pack up and go home, stay and boil the water, or hike for help. Suppose you considered packing up and hiking home and noticed that you could get very thirsty on the hike back. If you failed to notice that you definitely would get very thirsty in this situation, then you would have failed to
a. consider all the possible courses of action.
b. identify the consequences of the course of action.
c. evaluate the consequences of the course of action.
d. consider the probability that the consequences will occur.
1 Here are some helpful hints on this question. How expensive would a response be? What is to be gained from making contact? Could there be any danger involved?
2 Answer (c)