JEE Main · 2008 · 27 Apr 2008 · Offline · Mathematical Reasoning *

The statement $p\to (q\to p)$ is a tautology: whenever $p$ is false the whole conditional is true, and whenever $p$ is true the consequent $q\to p$ is true, so it holds in every case. Among the options, $p\to (p\vee q)$ is likewise always true, because if $p$ holds then $p\vee q$ holds, making that conditional a tautology as well. Being true in all cases, the two are equivalent.