GATE CS 2024 Set 2 Q2 — Propositional and First Order Logic

To represent the given English statement in propositional logic, let us break down its components:

• $p$: Fail grade can be given.
• $\neg p$: Fail grade cannot be given.
• $q$: Student scores more than $50 \%$ marks.

The given statement is: "Fail grade cannot be given when student scores more than $50 \%$ marks."

In English grammar and logic, a statement of the form "$X$ when $Y$" translates to the conditional statement "If $Y$, then $X$" (written as $Y \rightarrow X$).

Applying this translation to our statement:

• $Y$ (the condition) is: "student scores more than $50 \%$ marks", which is $q$.
• $X$ (the consequence) is: "Fail grade cannot be given", which is $\neg p$.

Thus, the logical representation is:

Therefore, the correct option is A.