Let p and q be the following propositions: p : Fail grade can be given. q : Student scores more than 50% marks. Consider the statement: 'Fail grade cannot be given when student scores more than 50% marks.' Which one of the following is the CORRECT representation of the above statement in propositional logic? A. q -> ~p B. ~q -> p C. p -> ~q D. ~p -> q

GATE 2024 · Discrete Mathematics · Propositional Logic · medium

Answer: q -> ~p, which is option A.

1. Identify the conditional structure: 'Fail grade cannot be given WHEN student scores more than 50% marks' => q -> ~p
2. Verify by checking options: q -> ~p: if q=T (high score) then ~p=T (no fail). If q=F (low score), the implication is vacuously true — we can still give a fail grade. This matches the English meaning exactly.