JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Mathematical Reasoning *

A tautology is always true. Grouping $(p\vee q)\vee (p\vee \sim q)=p\vee (q\vee \sim q)$, and since $q\vee \sim q$ is always true, the whole expression is $p\vee \text{T}=\text{T}$, a tautology. The others collapse to $p$, or to something equivalent to $(p\vee q)\wedge \sim (p\wedge q)$, none of which is true for every assignment.