Question at position 6 If Hans wins the marathon this year, then he is fit. But he is not fit. So he will not win the marathon this year. This is an example of a deductive and valid argument.TrueFalse单项选择题
A
True
B
False

Question

Question at position 6 If Hans wins the marathon this year, then he is fit. But he is not fit. So he will not win the marathon this year. This is an example of a deductive and valid argument.TrueFalse单项选择题

A

True

B

False

BlackTom AI · Accepted Answer

This argument is an instance of modus tollens: "If P then Q; not Q; therefore not P."

1. Relevant knowledge points and concepts
- Deductive argument: conclusion follows necessarily from premises.
- Validity: a deductive argument is valid when it is impossible for the premises to be true and the conclusion false at the same time.
- Modus tollens: a standard valid argument form with structure P → Q, ¬Q, therefore ¬P. Recognize also common invalid forms (affirming the consequent, denying the antecedent) to contrast.

2. Complete reasoning process step by step
- Symbolize: Let P = "Hans wins the marathon this year." Let Q = "Hans is fit."
- Premise 1: P → Q (If Hans wins then he is fit.)
- Premise 2: ¬Q (He is not fit.)
- From P → Q and ¬Q apply modus tollens to infer ¬P (Therefore, he will not win the marathon this year.)

3. Intermediate logical steps (showing why no counterexample exists)
- Assume both premises are true: P → Q is true and ¬Q is true (so Q is false).
- If Q is false while P → Q is true, P cannot be true — because if P were true, P → Q would force Q to be true, contradicting ¬Q.
- Therefore P must be false, i.e., ¬P is true. So with the premises true, the conclusion must also be true.

4. Why the correct answer is correct
- The pattern exactly matches modus tollens, a canonical valid deductive form. Validity depends on form, not on the actual truth of the premises. Because the conclusion necessarily follows from the premises, the argument is both deductive and valid.

5. Why the other option is incorrect
- Choosing "False" would assert that the argument is not a valid deductive instance. That is incorrect because the form P → Q; ¬Q; therefore ¬P is a textbook valid form (modus tollens). Confusion may arise with invalid forms like denying the antecedent (If P then Q; not P; therefore not Q), but that is not the form here.

6. Conclusion
- The argument is a deductive argument of the valid form modus tollens. Therefore the correct choice is True, which matches the provided answer.