Mathematical Reasoning: Negation of the Boolean expression pLeftrightarrow(qRightarrow p) is | JEE Main 2022

JEE Main 2022 (Online) 26th July Evening ShiftQuestion 1

Negation of the Boolean expression $p\Leftrightarrow(q\Rightarrow p)$ is

Mathematical Reasoning

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

Solution

$q\Rightarrow p\equiv\sim q\vee p$, so $p\Leftrightarrow(p\vee\sim q)$ is false only when $p=F,q=F$. Hence its negation is $\sim p\wedge\sim q$.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2022 (Online) 26th July Evening Shift)