MHTCET 19 Apr 2026 Shift 1 Paper

Concept:A tautology is a compound statement that is always true for all possible truth values of its variables.Explanation:Consider option A: $[(p \rightarrow q) \wedge \sim q] \rightarrow \sim p$.This statement is known as modus tollens.Using the equivalence $p \rightarrow q \equiv \sim p \vee q$, the antecedent becomes $(\sim p \vee q) \wedge \sim q$.If this antecedent is true, then $q$ is false, so $\sim p$ must be true.Thus, whenever the antecedent is true, the consequent $\sim p$ is also true, making the whole implication always true.So option A is a tautology.Now examine the other options.Option B is a contradiction, so it is always false.Option C simplifies to $(p \vee q) \wedge \sim(p \vee q)$, which is also a contradiction.In option D, the first bracket is a tautology, so the whole expression becomes $r$, which can be false.Therefore, only option A is always true.Answer:Option A: $[(p \rightarrow q) \wedge \sim q] \rightarrow \sim p$