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?
GATE CS - 2024,
Answer: A
The correct representation is \(q \to \neg p\).
'Fail grade cannot be given when student scores more than 50% marks' means: if the student scores more than 50% (\(q\)), then a fail grade cannot be given (\(\neg p\)). The 'when' clause is the condition, so it goes on the left of the implication.
\(q \to p\) says a fail grade can be given to such a student, the opposite. \(p \to q\) says that if a fail grade can be given then the student scored more than 50%, which reverses the direction and drops the negation. \(\neg p \to q\) is the converse of the correct statement, and an implication is not equivalent to its converse.
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