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?
Answer
(A)
Explanation
“\(X\) when \(Y\)” means “whenever \(Y\) holds, \(X\) holds”, which is the implication \(Y \rightarrow X\).
- The condition \(Y\) is “student scores more than 50% marks”, that is \(q\).
- The consequence \(X\) is “fail grade cannot be given”, that is \(\neg p\).
So the statement is \(q \rightarrow \neg p\). Option B drops the negation and says a fail grade can be given. Option D, \(\neg p \rightarrow q\), is the converse of \(q \rightarrow \neg p\) and is not equivalent to it, and option C has neither the right direction nor the negation.
Answer: A