JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Mathematical Reasoning *

An implication $X\Rightarrow Y$ is false only when X is true and Y is false. For the given statement to be false: $P\wedge (\sim R)$ must be true and $(\sim R)\wedge Q$ must be false. This gives $P\to T$, $R\to F$, $Q\to F$. Checking each option with these truth values:
(A) $T\vee F\to T$ is T
(B) $F\vee F\to F$ is T
(C) $\sim (T\vee F)\to T$ is T
(D) $\sim (F\vee F)\to F$ is $T\to F$ which is F.