MHTCET 17 Apr 2026 Shift 1 Paper

Concept:An implication $p \rightarrow (q \vee \sim r)$ is false only when $p$ is true and $(q \vee \sim r)$ is false.Explanation:Given $p \rightarrow (q \vee \sim r)$ is false, the antecedent $p$ must be true and the consequent must be false.So, $p = T$ and $q \vee \sim r = F$.A disjunction $q \vee \sim r$ is false only when both $q$ and $\sim r$ are false.Hence, $q = F$ and $\sim r = F$, which gives $r = T$.Thus, the truth values are $p = T$, $q = F$, $r = T$.Now evaluate $(p \leftrightarrow q) \wedge r$.Since $p = T$ and $q = F$, the biconditional $p \leftrightarrow q = F$.Therefore, $(p \leftrightarrow q) \wedge r = F \wedge T = F$.Next evaluate $\sim p \rightarrow \sim q$.Since $p = T$, we have $\sim p = F$.Since $q = F$, we have $\sim q = T$.So, $\sim p \rightarrow \sim q = F \rightarrow T = T$.The required truth values are $F$ and $T$ respectively.Answer:Option C: $F, T$