Question

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. $q \to \neg p$
• B. $q \to p$
• C. $p \to q$
• D. $\neg p \to q$

Hint:

To convert statements into propositional logic, carefully identify the conditional relationships and apply logical operators accordingly.

Answer 1

The Correct Option is A

The given statement can be interpreted as: $$\text{If a student scores more than \(50\%\) marks (\(q\)), then a fail grade (\(p\)) cannot be given (\(\neg p\)).}$$ This can be directly represented in propositional logic as: $$q \to \neg p$$ Validation of options:
(A) $q \to \neg p$: Correct. Matches the interpretation of the given statement.
(B) $q \to p$: Incorrect. This implies that scoring $>50\%$ leads to a fail grade.
(C) $p \to q$: Incorrect. This implies that failing implies scoring $>50\%$, which is incorrect.
(D) $\neg p \to q$: Incorrect. This implies that not failing implies scoring $>50\%$, which is not equivalent to the given statement. Final Answer: $$\boxed{q \to \neg p}$$