MHTCET 13 Apr 2026 Shift 1 Paper

Concept:A tautology is always true, and a contradiction is always false.We use logical equivalences to classify each statement pattern.Explanation:For A, $(q \rightarrow p) \vee (p \rightarrow q)$ becomes $(\sim q \vee p) \vee (\sim p \vee q)$.This simplifies to $(p \vee \sim p) \vee (q \vee \sim q)$, which is always true.So A is a tautology.For B, $(\sim p \vee \sim q) \leftrightarrow \sim(p \wedge q)$.By De Morgan's law, $\sim(p \wedge q) \equiv \sim p \vee \sim q$.Both sides of the biconditional are identical, so B is always true.Hence, B is a tautology.For C, $[(p \vee q) \wedge \sim p] \wedge \sim q$ can be rewritten as $(p \vee q) \wedge (\sim p \wedge \sim q)$.Since $\sim p \wedge \sim q \equiv \sim(p \vee q)$, the expression becomes $(p \vee q) \wedge \sim(p \vee q)$, which is always false.So C is a contradiction.For D, $(p \wedge q) \wedge (\sim p \vee \sim q)$.Here $\sim p \vee \sim q \equiv \sim(p \wedge q)$.So the expression becomes $(p \wedge q) \wedge \sim(p \wedge q)$, which is always false.Hence, D is a contradiction.Answer:A and B are tautologies, while C and D are contradictions.Therefore, the correct option is Option B.