JEE Main 2013 (Online) 9th AprilQuestion 1
Statement-1: The statement $A\to(B\to A)$ is equivalent to $A\to(A\vee B)$.
Statement-2: The statement $\sim\left[(A\wedge B)\to(\sim A\vee B)\right]$ is a Tautology.
Sets, Relations and Function
Solution
$A\to(B\to A)$ and $A\to(A\vee B)$ are both tautologies, hence equivalent. $(A\wedge B)\to(\sim A\vee B)$ is a tautology since $A\wedge B$ forces $B$, so its negation is a fallacy. Statement-1 true, Statement-2 false.