JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Mathematical Reasoning *

Build the truth table of $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$. When $p$ is true it fails — one of the two implications is false — while for both cases with $p$ false the conjunction is true. So the statement is true exactly when $p$ is false, making it equivalent to $\sim p$.