Q: Which of the following argument forms is known as modus ponens?

$$\text{If P then Q. P. Therefore, Q.}$$

Q: Which of the following is an example of the fallacy known as 'affirming the consequent'?

$$\text{If Jane lives in Beijing, then Jane lives in China. Jane lives in China. Therefore, Jane lives in Beijing.}$$

Q: Which of the following argument forms is modus tollens?

$$\text{If P then Q. Not Q. Therefore, not P.}$$

Q: Suppose you want to prove that a certain statement $$S is $$false by showing that assuming $$S$$ leads to a contradiction. Which valid argument pattern are you using?

$$\text{Reductio ad Absurdum}$$

Q: Which of the following is a valid form of disjunctive syllogism?

$$\text{P or Q. Not P. Therefore, Q.}$$

Q: Which of the following is an example of a dilemma argument?

$$\text{Either we increase the tax rate or we don't. If we do, people will be unhappy. If we don't, people will also be unhappy. Therefore, people are going to be unhappy anyway.}$$

Q: Which of the following is a valid hypothetical syllogism?

$$\text{If P then Q. If Q then R. Therefore, if P then R.}$$

Q: Which of the following is NOT a valid argument form?

$$\text{If P then Q. Q. Therefore, P.}$$

Q: A student claims: 'If it rains, the ground will be wet. The ground is wet. Therefore, it rained.' What logical fallacy is being committed?

$$\text{Affirming the consequent}$$

Q: Which of the following best illustrates the use of 'reductio ad absurdum' in a real-world context?

$$\text{Suppose someone claims that nothing is true for sure. If that were true, then the claim itself would not be true for sure, which is a contradiction. Therefore, the claim must be false.}$$

Question 1

Which of the following argument forms is known as modus ponens?

Accepted Answer

$$	ext{If P then Q. P. Therefore, Q.}$$

Question 2

Which of the following is an example of the fallacy known as 'affirming the consequent'?

Accepted Answer

$$	ext{If Jane lives in Beijing, then Jane lives in China. Jane lives in China. Therefore, Jane lives in Beijing.}$$

Question 3

Which of the following argument forms is modus tollens?

Accepted Answer

$$	ext{If P then Q. Not Q. Therefore, not P.}$$

Question 4

Suppose you want to prove that a certain statement $$S is $$false by showing that assuming $$S$$ leads to a contradiction. Which valid argument pattern are you using?

Accepted Answer

$$	ext{Reductio ad Absurdum}$$

Question 5

Which of the following is a valid form of disjunctive syllogism?

Accepted Answer

$$	ext{P or Q. Not P. Therefore, Q.}$$

Question 6

Which of the following is an example of a dilemma argument?

Accepted Answer

$$	ext{Either we increase the tax rate or we don't. If we do, people will be unhappy. If we don't, people will also be unhappy. Therefore, people are going to be unhappy anyway.}$$

Question 7

Which of the following is a valid hypothetical syllogism?

Accepted Answer

$$	ext{If P then Q. If Q then R. Therefore, if P then R.}$$

Question 8

Which of the following is NOT a valid argument form?

Accepted Answer

$$	ext{If P then Q. Q. Therefore, P.}$$

Question 9

A student claims: 'If it rains, the ground will be wet. The ground is wet. Therefore, it rained.' What logical fallacy is being committed?

Accepted Answer

$$	ext{Affirming the consequent}$$

Question 10

Which of the following best illustrates the use of 'reductio ad absurdum' in a real-world context?

Accepted Answer

$$	ext{Suppose someone claims that nothing is true for sure. If that were true, then the claim itself would not be true for sure, which is a contradiction. Therefore, the claim must be false.}$$

Question 11

Which of the following is a valid argument form that can be constructed by combining two cases of hypothetical syllogism?

Accepted Answer

$$	ext{If P then Q. If Q then R. If R then S. Therefore, if P then S.}$$

Question 12

Which of the following is a valid argument form for 'P and Q. Therefore Q.'?

Accepted Answer

$$	ext{Conjunction elimination}$$

Question 13

Which of the following is an example of denying the antecedent, which is an invalid argument form?

Accepted Answer

$$	ext{If P then Q. Not P. Therefore, not Q.}$$

Question 14

In a real-world scenario, which of the following best illustrates a disjunctive syllogism?

Accepted Answer

$$	ext{Either the train is late or it has already left. The train is not late. Therefore, it has already left.}$$

Question 15

Which of the following is a valid argument form for 'P. Therefore, P.'?

Accepted Answer

$$	ext{Repetition (tautology)}$$

Question 16

Which of the following is a valid argument form for 'P or Q. Q. Therefore, P.'?

Accepted Answer

$$	ext{This is not a valid argument form}$$

Question 17

Which of the following best describes the difference between a valid argument and a sound argument?

Accepted Answer

$$	ext{A valid argument has a correct logical form, while a sound argument is valid and has all true premises.}$$

Valid Patterns of Deductive Reasoning: Study Notes for Critical Thinking and Logic

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