Question at position 20 Consider the following premises: Premises: P1: Li Wei will either attend the lecture or watch the recorded class online. P2: Li Wei did not attend the lecture. Which of the following statements necessarily follows from the premises?Li Wei will watch the recorded class online.Li Wei might watch the recording.Li Wei did both.No valid conclusion follows.单项选择题
A
Li Wei will watch the recorded class online.
B
Li Wei might watch the recording.
C
Li Wei did both.
D
No valid conclusion follows.

Question

Question at position 20 Consider the following premises: Premises: P1: Li Wei will either attend the lecture or watch the recorded class online. P2: Li Wei did not attend the lecture. Which of the following statements necessarily follows from the premises?Li Wei will watch the recorded class online.Li Wei might watch the recording.Li Wei did both.No valid conclusion follows.单项选择题

A

Li Wei will watch the recorded class online.

B

Li Wei might watch the recording.

C

Li Wei did both.

D

No valid conclusion follows.

BlackTom AI · Accepted Answer

Disjunctive syllogism applies: from "A or B" together with "not A" we can conclude B.

1. Relevant knowledge points and concepts
- Propositional logic: let A = "Li Wei attends the lecture" and B = "Li Wei watches the recorded class online."
- Disjunction (A ∨ B) means at least one of A or B is true (inclusive or); in common-language "either...or" can be exclusive, but either reading still supports the same inference here.
- Disjunctive syllogism: from A ∨ B and ¬A infer B.

2. Step-by-step reasoning
- P1 states A ∨ B (Li Wei attends OR watches the recording).
- P2 states ¬A (Li Wei did not attend).
- Apply disjunctive syllogism: given A ∨ B and ¬A, B must be true.

3. Intermediate logical steps (formal)
- P1: A ∨ B
- P2: ¬A
- From P1 and P2: B (by disjunctive syllogism / disjunction elimination)

4. Why the correct answer is correct
- If at least one of the two options is true (P1) and one option (attending) is ruled out (P2), the remaining option (watching the recorded class) must be true. This is a valid, necessary logical consequence of the premises.

5. Why the other options are incorrect
- "Li Wei might watch the recording." This is weaker than the necessary conclusion; the premises force B true, not merely possible.
- "Li Wei did both." This contradicts P2, which explicitly denies attendance, so "both" is impossible.
- "No valid conclusion follows." Incorrect because a valid conclusion (B) does follow by a standard logical rule.

6. Conclusion
Therefore, the necessary conclusion is "Li Wei will watch the recorded class online." This matches the provided correct answer.

类似问题

Let [math: A] and [math: B] be sets. If [math: p] is the proposition "[math: x∈A]" and [math: q] is the proposition "[math: x∈B]", which of the following is logically equivalent to "[math: x∈A∪B]"?

Consider the sentences [math: ¬((p→¬q)∧r)] and [math: (p∧q)∨¬r]. There are 8 possible interpretations for these sentences according to the truth values of [math: p], [math: q] and [math: r]. Under how many of these interpretations do the two sentences have the same truth value?

Which of the following expressions is a tautology?[Fill in the blank]

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

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