JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Mathematical Reasoning *

A tautology is a statement true for every assignment of truth values to its components. The expression $[A\wedge (A\to B)]\to B$ encodes modus ponens: whenever both $A$ and $A\to B$ are true, $B$ is true, so the antecedent $A\wedge (A\to B)$ can be true only when $B$ is already true, and in every other case the antecedent is false. An implication with this property is never false, so this compound statement is always true and is the tautology among the given statements.