Let p, q, r denote the statements 'It is raining', 'It is cold', and 'It is pleasant', respectively. Then the statement 'It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold' is represented by A. (~p /\ r) /\ (~r -> (p /\ q)) B. (~p /\ r) /\ ((p /\ q) -> ~r) C. (~p /\ r) /\ ((p /\ q) -> r) D. (~p /\ r) /\ (~r -> (p \/ q))

GATE 2017 · Discrete Mathematics · Propositional Logic · medium

Answer: (~p /\ r) /\ (~r -> (p /\ q))

1. Translate first clause: 'It is not raining and it is pleasant' = ~p /\ r
2. Translate the 'only if' clause: 'It is not pleasant only if it is raining and it is cold' = ~r -> (p /\ q)
3. Conjoin both parts: (~p /\ r) /\ (~r -> (p /\ q))