SOLUTIONS MANUAL
** All Chapters included
,Table of Contents are given below
Chapter 1: Thinking Critically
Chapter 2: Approaches to Problem Solving
Chapter 3: Numbers in the Real World
Chapter 4: Managing Money
Chapter 5: Statistical Reasoning
Chapter 6: Putting Statistics to Work
Chapter 7: Probability: Living with the Odds
Chapter 8: Exponential Astonishment
Chapter 9: Modeling Our World
Chapter 10: Modeling with Geometry
Chapter 11: Mathematics and the Arts
Chapter 11 Review Questions
Chapter 12: Mathematics and Politics
,Chapter 1: Thinking Critically
UNIT 1A: LIVING IN THE MEDIA AGE
THINK ABOUT IT
Pg. 21. Not guilty does not mean innocent; it means not enough evidence to prove guilt. If defendants were
required to prove innocence, there would be many cases where they would be unable to provide such proof even
though they were, in fact, innocent. This relates to the fallacy of appeal to ignorance in the sense that lack of
proof of guilt does not mean innocence, and lack of proof of innocence does not mean guilt.
Pg. 23. Opinions will vary. One argument is that character questions should be allowed in court if answers to
those questions may show bias or ulterior motives for testimony given by a witness. This would be a good topic
for a discussion either during or outside of class.
Pg. 25. Answers may vary. Cybercriminals used deepfakes of a public figure to promote fake cryptocurrency
investments in 2025. Unrealistic investment promises are a clear sign that this is scam.
QUICK QUIZ
QQ1. a. By the definition used in this book, an argument always contains at least one premise and a conclusion.
QQ2. c. By definition, a fallacy is a deceptive argument.
QQ3. b. An argument must contain a conclusion.
QQ4. a. Circular reasoning is an argument where the premise and the conclusion say essentially the same thing.
QQ5. b. Using the fact that a statement is unproved to imply that it is false is appeal to ignorance.
QQ6. b. “I don’t support the President’s tax plan” is the conclusion because the premise “I don’t trust his motives”
supports that conclusion.
QQ7. b. This is a personal attack because the premise (I don’t trust his motives) attacks the character of the
President, and says nothing about the substance of his tax plan.
QQ8. c. This is limited choice because the argument does not allow for the possibility that you are a fan of, say,
boxing.
QQ9. b. Just because A preceded B does not necessarily imply that A caused B.
QQ10. a. By definition, a straw man is an argument that distorts (or misrepresents) the real issue.
READING QUESTIONS
1. Logic is the study of the methods and principles of reasoning. Arguing logically may or may not change a
person’s position, but it can give either person insight into the other’s thinking.
2. An argument refers to a reasoned or thoughtful process. An argument uses a set of facts or assumptions,
called premises, to support a conclusion.
3. A fallacy is an argument in which the conclusion is not well supported by the premises. The examples of
fallacies given in the text are appeal to popularity, false cause, appeal to ignorance, hasty generalization,
limited choice, appeal to emotion, personal attack, circular reasoning, diversion (red herring), and straw
man. Examples will vary.
4. Deepfakes are videos, images, or audio made with AI to look real. It is important to aware, because many
deepfakes have some type of distortion that you might recognize, or they may have a context that simply
, does not make sense.
5. AI hallucinations happen when an AI gives detailed but false information. For example, a citation to 3
scientific papers that sounds real but does not exist and the journal was real, but no paper with the given
title had ever been published, and none of the listed authors were real people. It is important to be aware
because AI may make detailed but false claims.
6. The five steps (See the information box on page 24 in the text for a summary of each step.) to evaluating
media information are:
1. Consider the source.
2. Check the date.
3. Validate accuracy.
4. Watch for hidden agendas.
5. Don’t miss the big picture.
DOES IT MAKE SENSE?
7. Does not make sense. Raising one’s voice has nothing to do with logical arguments.
8. Does not make sense. Logical arguments always contain at least one premise and a conclusion.
9. Makes sense. A logical person would not put much faith in an argument that uses premises he believes to
be false to support a conclusion.
10. Makes sense. There’s nothing wrong with stating the conclusion of an argument before laying out the
premises.
11. Does not make sense. One can disagree with the conclusion of a well-stated argument regardless of
whether it is fallacious.
12. Does not make sense. Even sophisticated AI can provide incorrect or misleading answers due to
limitations in data, algorithms, or understanding, so their answers are not always trustworthy.
BASIC SKILLS AND CONCEPTS
13. a. Premise: Apple’s iPhone outsells all other smartphones. Conclusion: They must be the best
smartphone on the market.
b. The fact that many people buy the iPhone does not necessarily mean it is the best smartphone.
14. a. Premise: I became sick soon after eating at Burger Hut. Conclusion: Burger Hut food made me
sick.
b. The argument doesn’t prove that Burger Hut food was the cause of the sickness.
15. a. Premise: Decades of searching have not revealed life on other planets. Conclusion: Life in the
universe must be confined to Earth.
b. Failure to find life on other planets does not imply that life does not exist elsewhere in the
universe.
16. a. Premise: I saw three people use food stamps to buy expensive steaks. Conclusion: Abuse of food
stamps is widespread.
b. The conclusion is based on relatively little evidence.
** All Chapters included
,Table of Contents are given below
Chapter 1: Thinking Critically
Chapter 2: Approaches to Problem Solving
Chapter 3: Numbers in the Real World
Chapter 4: Managing Money
Chapter 5: Statistical Reasoning
Chapter 6: Putting Statistics to Work
Chapter 7: Probability: Living with the Odds
Chapter 8: Exponential Astonishment
Chapter 9: Modeling Our World
Chapter 10: Modeling with Geometry
Chapter 11: Mathematics and the Arts
Chapter 11 Review Questions
Chapter 12: Mathematics and Politics
,Chapter 1: Thinking Critically
UNIT 1A: LIVING IN THE MEDIA AGE
THINK ABOUT IT
Pg. 21. Not guilty does not mean innocent; it means not enough evidence to prove guilt. If defendants were
required to prove innocence, there would be many cases where they would be unable to provide such proof even
though they were, in fact, innocent. This relates to the fallacy of appeal to ignorance in the sense that lack of
proof of guilt does not mean innocence, and lack of proof of innocence does not mean guilt.
Pg. 23. Opinions will vary. One argument is that character questions should be allowed in court if answers to
those questions may show bias or ulterior motives for testimony given by a witness. This would be a good topic
for a discussion either during or outside of class.
Pg. 25. Answers may vary. Cybercriminals used deepfakes of a public figure to promote fake cryptocurrency
investments in 2025. Unrealistic investment promises are a clear sign that this is scam.
QUICK QUIZ
QQ1. a. By the definition used in this book, an argument always contains at least one premise and a conclusion.
QQ2. c. By definition, a fallacy is a deceptive argument.
QQ3. b. An argument must contain a conclusion.
QQ4. a. Circular reasoning is an argument where the premise and the conclusion say essentially the same thing.
QQ5. b. Using the fact that a statement is unproved to imply that it is false is appeal to ignorance.
QQ6. b. “I don’t support the President’s tax plan” is the conclusion because the premise “I don’t trust his motives”
supports that conclusion.
QQ7. b. This is a personal attack because the premise (I don’t trust his motives) attacks the character of the
President, and says nothing about the substance of his tax plan.
QQ8. c. This is limited choice because the argument does not allow for the possibility that you are a fan of, say,
boxing.
QQ9. b. Just because A preceded B does not necessarily imply that A caused B.
QQ10. a. By definition, a straw man is an argument that distorts (or misrepresents) the real issue.
READING QUESTIONS
1. Logic is the study of the methods and principles of reasoning. Arguing logically may or may not change a
person’s position, but it can give either person insight into the other’s thinking.
2. An argument refers to a reasoned or thoughtful process. An argument uses a set of facts or assumptions,
called premises, to support a conclusion.
3. A fallacy is an argument in which the conclusion is not well supported by the premises. The examples of
fallacies given in the text are appeal to popularity, false cause, appeal to ignorance, hasty generalization,
limited choice, appeal to emotion, personal attack, circular reasoning, diversion (red herring), and straw
man. Examples will vary.
4. Deepfakes are videos, images, or audio made with AI to look real. It is important to aware, because many
deepfakes have some type of distortion that you might recognize, or they may have a context that simply
, does not make sense.
5. AI hallucinations happen when an AI gives detailed but false information. For example, a citation to 3
scientific papers that sounds real but does not exist and the journal was real, but no paper with the given
title had ever been published, and none of the listed authors were real people. It is important to be aware
because AI may make detailed but false claims.
6. The five steps (See the information box on page 24 in the text for a summary of each step.) to evaluating
media information are:
1. Consider the source.
2. Check the date.
3. Validate accuracy.
4. Watch for hidden agendas.
5. Don’t miss the big picture.
DOES IT MAKE SENSE?
7. Does not make sense. Raising one’s voice has nothing to do with logical arguments.
8. Does not make sense. Logical arguments always contain at least one premise and a conclusion.
9. Makes sense. A logical person would not put much faith in an argument that uses premises he believes to
be false to support a conclusion.
10. Makes sense. There’s nothing wrong with stating the conclusion of an argument before laying out the
premises.
11. Does not make sense. One can disagree with the conclusion of a well-stated argument regardless of
whether it is fallacious.
12. Does not make sense. Even sophisticated AI can provide incorrect or misleading answers due to
limitations in data, algorithms, or understanding, so their answers are not always trustworthy.
BASIC SKILLS AND CONCEPTS
13. a. Premise: Apple’s iPhone outsells all other smartphones. Conclusion: They must be the best
smartphone on the market.
b. The fact that many people buy the iPhone does not necessarily mean it is the best smartphone.
14. a. Premise: I became sick soon after eating at Burger Hut. Conclusion: Burger Hut food made me
sick.
b. The argument doesn’t prove that Burger Hut food was the cause of the sickness.
15. a. Premise: Decades of searching have not revealed life on other planets. Conclusion: Life in the
universe must be confined to Earth.
b. Failure to find life on other planets does not imply that life does not exist elsewhere in the
universe.
16. a. Premise: I saw three people use food stamps to buy expensive steaks. Conclusion: Abuse of food
stamps is widespread.
b. The conclusion is based on relatively little evidence.
