JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q17

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MathematicsSingle correct+4 / -1Question 17 of 90

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

(\sim p)\wedge q

p\wedge(\sim q)

(\sim p)\vee(\sim q)

(\sim p)\wedge(\sim q)

Answer and worked solution

Official answer: D

Simplify. If p is true, both sides are true. If p is false, $q\Rightarrow p$ is $\sim q$ , and $F\Leftrightarrow\sim q$ is true exactly when q is true. So the statement is $p\vee q$ .

Negation $(\sim p)\wedge(\sim q)$ . (D)

Topics:Mathematical reasoning

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JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 17