MHTCET 5 May 2025 Shift 2 Paper

Concept:The negation of an implication is obtained by applying logical equivalences like the conditional law and De Morgan's laws. Since the given statement is a tautology, its negation must be a contradiction.Explanation:Let the given statement pattern be $S = (p \wedge \sim q) \rightarrow (p \vee \sim q)$.We need to find $\sim S$.Using the conditional law, $A \rightarrow B \equiv \sim A \vee B$, we get:$\sim S \equiv \sim[\sim(p \wedge \sim q) \vee (p \vee \sim q)]$Now apply De Morgan's law:$\sim S \equiv (p \wedge \sim q) \wedge \sim(p \vee \sim q)$Applying De Morgan's law again:$\sim S \equiv (p \wedge \sim q) \wedge (\sim p \wedge q)$Using associative and commutative laws:$\sim S \equiv (p \wedge \sim p) \wedge (\sim q \wedge q)$By the complement law, $p \wedge \sim p \equiv F$ and $\sim q \wedge q \equiv F$.Therefore, $\sim S \equiv F \wedge F \equiv F$.So the negation is always false, which is the definition of a contradiction.Answer:The negation of the given statement pattern is a contradiction. The correct option is C.