She chats on her mobile only when her boss is away for lunch. A. The boss is…

Concept: A statement of the form ‘X only when Y’ means X occurs only if Y holds, i.e. X → Y (Y is a necessary condition for X). For any conditional P → Q, only its contrapositive, ¬Q → ¬P, is guaranteed to be logically equivalent; the converse (Q → P) and the inverse (¬P → ¬Q) are NOT guaranteed to hold.

Application: Let C = ‘She chatted on her mobile’ and A = ‘The boss is away for lunch’. The statement ‘She chats only when her boss is away’ gives C → A. Its contrapositive is ¬A → ¬C, i.e. D → B (using D = ‘The boss is not away for lunch’ and B = ‘She did not chat on her mobile’). Since a contrapositive is always logically equivalent to the original conditional, D → B is a valid inference — this is exactly the pairing given by DB.

• AB (A → B): being told the boss is away only tells us a necessary condition is met; it does not force any conclusion about whether she chatted, so A does not imply B.

• DC (D → C): this reverses the necessary condition — since chatting requires the boss to be away, the boss not being away rules out chatting rather than confirming it, so D cannot imply C.

• BC (B → C): this asserts that not chatting implies chatting, a direct contradiction, so it can never be a valid inference.

Hence, the only pairing that logically follows from the given statement is the contrapositive pairing DB.