JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Mathematical Reasoning *

Suppose the antecedent $(P\Rightarrow Q)\wedge \sim Q$ is true. Then $P\Rightarrow Q$ holds while $Q$ is false, which forces $P$ to be false, so $\sim P$ is true. When the antecedent is false the implication is true in any case, so

is true in every row of the truth table. Replacing the consequent by $Q$, by $P\wedge Q$ or by $P$ fails, because in exactly the rows where the antecedent is true, $Q$ is false, $P$ is false and so $P\wedge Q$ is false as well. The tautology is $\left((P\Rightarrow Q)\wedge \sim Q\right)\Rightarrow \sim P$.