JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Mathematical Reasoning *

Simplify $\sim (p\vee \sim q)$ by De Morgan's law to $\sim p\wedge q$, so the statement becomes $(\sim p\wedge q)\to (p\vee q)$. Whenever the antecedent $\sim p\wedge q$ is true, $q$ is true, which makes $p\vee q$ true; and whenever the antecedent is false the implication is automatically true. Being true in every case, the statement is a tautology.