Mathematical Reasoning: The statement among the following that is a tautology is : | JEE Main 2021

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 1

The statement among the following that is a tautology is :

Mathematical Reasoning

$A\wedge(A\vee B)$$A\vee(A\wedge B)$$[A\wedge(A\to B)]\to B$✓ Correct answer$B\to[A\wedge(A\to B)]$

Solution

$[A\wedge(A\to B)]\to B$ is modus ponens: if $A$ and $A\to B$ hold then $B$ holds, so it is always true. The others fail for $A=F$ or $B=T,A=F$.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2021 (Online) 24th February Morning Shift)