JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Mathematical Reasoning *

Test the compound statement $\left(p\to (q\to p)\right)\to \left(p\to (p\vee q)\right)$ over every truth assignment. Whenever $p$ is true, both $q\to p$ and $p\vee q$ are true, so each implication built on $p$ holds; whenever $p$ is false, every implication with $p$ as antecedent is vacuously true. Running through all four combinations of $p$ and $q$, the statement is true in each case, so it is a tautology.