Conditional "only when": Premise: "He wears a jacket only when she goes to a party." Choose the pair that must hold (logically follows) under this premise.
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A(ii) She went to a party. (iii) He wore a jacket.
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B(i) She did not go to a party. (iv) He did not wear a jacket.
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C(iii) He wore a jacket. (i) She did not go to a party.
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D(iv) He did not wear a jacket. (i) She did not go to a party.
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ENone of these
Answer
Correct Answer: (i) She did not go to a party. (iv) He did not wear a jacket.
Explanation
Introduction / Context:"Only when" indicates necessity. "He wears a jacket only when she goes to a party" translates to: If he wears a jacket, then she goes to a party (Wear ⇒ Party).
Given Data / Assumptions:
- (i) She did not go to a party.
- (ii) She went to a party.
- (iii) He wore a jacket.
- (iv) He did not wear a jacket.
Concept / Approach:From Wear ⇒ Party, take the contrapositive: ¬Party ⇒ ¬Wear. This is the only direction that is guaranteed besides the original implication. The converse (Party ⇒ Wear) is not guaranteed.
Step-by-Step Solution:
If (i) is true (she did not go), then by contrapositive (iv) must be true (he did not wear).Pairs that assert (ii) and (iii) together are only consistent, not necessary: the premise allows parties without jackets.Verification / Alternative check:Truth table confirms that ¬Party ⇒ ¬Wear must hold whenever the premise holds.
Why Other Options Are Wrong:
- (a) could be true but is not forced by the premise.
- (c) contradicts the premise (wearing with no party).
- (d) duplicates (b) order but key uses (b) as canonical.
- None of these is wrong because (b) is compelled by logic.
Common Pitfalls:Confusing necessity with sufficiency; assuming party ⇒ jacket.
Final Answer:(i) and (iv)