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.

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:

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)