JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Mathematical Reasoning *

The antecedent $(P\vee Q)\wedge (\sim P)$ is true only when $P$ is false and $Q$ is true, and in that case the consequent $Q$ is true as well, so the implication is true in every row: it is a tautology.
An equivalent compound statement must therefore be a tautology too. Since $\sim (P\Rightarrow Q)$ and $P\wedge \sim Q$ agree in all four rows, the biconditional $\sim (P\Rightarrow Q)\iff P\wedge \sim Q$ is a tautology, whereas $P\vee Q$, $P\wedge \sim Q$ and $\sim (P\Rightarrow Q)$ are each false when $P$ and $Q$ are both false.
So the given statement is equivalent to $\sim (P\Rightarrow Q)\iff P\wedge \sim Q$.