MHTCET 16 Apr 2026 Shift 2 Paper

Concept:For an implication $A \rightarrow B$, the contrapositive is $\sim B \rightarrow \sim A$.The negation of an implication $r \rightarrow s$ is $r \wedge \sim s$.Explanation:Let $A = p \vee \sim q$ and $B = p \wedge \sim q$.The given statement is $A \rightarrow B$.Its contrapositive is $\sim B \rightarrow \sim A$.So, the contrapositive is $\sim(p \wedge \sim q) \rightarrow \sim(p \vee \sim q)$.Now negate this contrapositive:$\sim[\sim(p \wedge \sim q) \rightarrow \sim(p \vee \sim q)]$.Using negation of an implication, this becomes:$\sim(p \wedge \sim q) \wedge \sim[\sim(p \vee \sim q)]$.Using double negation, $\sim[\sim(p \vee \sim q)] = p \vee \sim q$.So, the expression becomes $\sim(p \wedge \sim q) \wedge (p \vee \sim q)$.By De Morgan's law, $\sim(p \wedge \sim q) = \sim p \vee q$.Therefore, the required expression is $(\sim p \vee q) \wedge (p \vee \sim q)$.Answer:$(\sim p \vee q) \wedge (p \vee \sim q)$Hence, the correct option is D.