GATE CS 2024 Set 2 Q.12: Propositional and First-Order Logic

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?

$q \rightarrow \neg p$

$q \rightarrow p$

$p \rightarrow q$

$\neg p \rightarrow q$

Official answer and solution

Official answer: A
From: Official GATE 2024 answer key

Solution

Translate 'A when B' into the implication $B \rightarrow A$ .

In the statement 'Fail grade cannot be given ( $\neg p$ ) when student scores more than 50% marks ( $q$ )', the condition 'when student scores more than 50% marks' ( $q$ ) is the antecedent, and 'Fail grade cannot be given' ( $\neg p$ ) is the consequent:

q \rightarrow \neg p

Final answer

Option (A)

Common trap

Reversing the implication to $\neg p \rightarrow q$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 2 (CS2)
Question: 12 of 65
Section: Computer Science and Information Technology

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