JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Mathematical Reasoning *

A tautology is true for every assignment of $p$ and $q$, so hunt for the one that can fail. The statements $(p\wedge q)\to p$, $p\to (p\vee q)$ and $(p\wedge q)\to (\sim p\vee q)$ all simplify to $T$, so they are tautologies. But $(p\vee q)\to (p\vee \sim q)$ fails: take $p$ false and $q$ true, then the left side $p\vee q$ is true while the right side $p\vee \sim q$ is false, making the implication false. So the statement $(p\vee q)\to (p\vee \sim q)$ is not a tautology.