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: \[ \boxed{q \to \neg p} \]