Sets, Relations and Function: The negation of the expression qvee ((sim q)wedge p ) is equivalent to | JEE Main 2023

JEE Main 2023 (Online) 1st February Morning ShiftQuestion 1

The negation of the expression $q\vee\left((\sim q)\wedge p\right)$ is equivalent to

Sets, Relations and Function

$(\sim p)\wedge(\sim q)$✓ Correct answer$p\wedge(\sim q)$$(\sim p)\vee(\sim q)$$(\sim p)\vee q$

Solution

$q\vee(\sim q\wedge p)=(q\vee\sim q)\wedge(q\vee p)=p\vee q$, so its negation is $(\sim p)\wedge(\sim q)$.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2023 (Online) 1st February Morning Shift)