JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Mathematical Reasoning *

An implication is false only when its hypothesis is true and its conclusion false. So $p\to (p\wedge \sim q)$ being false forces $p$ to be true and $p\wedge \sim q$ to be false. With $p$ true, $p\wedge \sim q$ can fail only if $\sim q$ is false, meaning $q$ is true. Hence $p$ and $q$ are both true.