JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Mathematical Reasoning *

A tautology is true for every assignment of truth values. The statement $(P\wedge (P\to Q))\to Q$ is the modus ponens form: whenever $P\wedge (P\to Q)$ is true both $P$ and $P\to Q$ hold, which forces $Q$ to be true, and whenever the antecedent is false the implication is vacuously true. Being true in every case, it is a tautology, while the other candidates collapse to $P$ by the absorption laws or fail for some assignment.