Question at position 16 Argument:P1: If time is managed well, stress is reduced.P2: Stress is reduced.C: Therefore, time was managed well. Question: Identify the argument type: Valid (Modus Tollens)Invalid (Affirming the consequent)Invalid (Denying the antecedent)Valid (Modus Ponens)单项选择题
A
Valid (Modus Tollens)
B
Invalid (Affirming the consequent)
C
Invalid (Denying the antecedent)
D
Valid (Modus Ponens)

Question

Question at position 16 Argument:P1: If time is managed well, stress is reduced.P2: Stress is reduced.C: Therefore, time was managed well. Question: Identify the argument type: Valid (Modus Tollens)Invalid (Affirming the consequent)Invalid (Denying the antecedent)Valid (Modus Ponens)单项选择题

A

Valid (Modus Tollens)

B

Invalid (Affirming the consequent)

C

Invalid (Denying the antecedent)

D

Valid (Modus Ponens)

BlackTom AI · Accepted Answer

Affirming the consequent is the correct identification because the argument has the form If T then S; S; therefore T.

1. Relevant knowledge points and concepts
- Propositional conditional: "If P then Q" written P → Q.
- Valid deductive forms: Modus Ponens (P → Q; P; therefore Q) and Modus Tollens (P → Q; ¬Q; therefore ¬P).
- Common invalid forms: Affirming the consequent (P → Q; Q; therefore P) and Denying the antecedent (P → Q; ¬P; therefore ¬Q).
- Validity means: whenever the premises are true, the conclusion must be true.

2. Step‑by‑step mapping of this argument
- Let T = "time is managed well"
- Let S = "stress is reduced"
- Premise 1: If time is managed well, stress is reduced → T → S
- Premise 2: Stress is reduced → S
- Conclusion: Therefore, time was managed well → T
- Symbolic form: (T → S), S ⊢ T

3. Intermediate truth-value demonstration (counterexample)
- Choose truth values: T = false, S = true.
- Evaluate premise T → S: false → true is true.
- Premise S is true by choice.
- Conclusion T is false.
- Both premises are true while the conclusion is false, so the argument is invalid.

4. Why the correct answer is correct
- The form (T → S; S; therefore T) is exactly the pattern called affirming the consequent. That pattern does not guarantee the truth of the antecedent just because the consequent holds; other causes can make S true. The truth-value counterexample shows the premises true with a false conclusion, proving invalidity.

5. Why the other options are incorrect
- Valid (Modus Tollens): would require (T → S; ¬S; therefore ¬T) — not the case here.
- Invalid (Denying the antecedent): would be (T → S; ¬T; therefore ¬S) — not the case.
- Valid (Modus Ponens): would be (T → S; T; therefore S) — not the case.