Sets, Relations and Function: The statement BRightarrow ((sim A)vee B ) is not equivalent to : | JEE Main 2023

JEE Main 2023 (Online) 29th January Evening ShiftQuestion 1

The statement $B\Rightarrow\left((\sim A)\vee B\right)$ is not equivalent to :

Sets, Relations and Function

$B\Rightarrow(A\Rightarrow B)$$A\Rightarrow(A\Leftrightarrow B)$✓ Correct answer$A\Rightarrow((\sim A)\Rightarrow B)$$B\Rightarrow((\sim A)\Rightarrow B)$

Solution

$B\Rightarrow(\sim A\vee B)$ is a tautology. Options A, C, D are also tautologies, but $A\Rightarrow(A\Leftrightarrow B)=\sim A\vee B$ is false for $A=T,B=F$, so it is not equivalent.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2023 (Online) 29th January Evening Shift)

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