QJEEM22Mab6e6: JEE Main 2022 Mathematics - Class 11 JEEM22Mab6e6 Solution: Negation of the Boolean expression p ⇔ ( q ⇒ p ) is

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

$p \Leftrightarrow (q \Rightarrow p)$

$\sim (p \Leftrightarrow (q \Leftrightarrow p))$

$\equiv p \Leftrightarrow \sim (q \Rightarrow p)$

$\equiv p \Leftrightarrow (q \land \sim p)$

$\equiv (p \Rightarrow (q \land \sim p)) \land ((q \land \sim p) \Rightarrow p))$

$\equiv (\sim p \lor (q \land \sim p)) \land ((\sim q \lor p) \lor p))$

$\equiv ((\sim p \lor q) \land \sim p) \land (\sim q \lor p)$

$\equiv\sim p \land (\sim q \lor p)$

$\equiv (\sim p \land \sim q) \lor (\sim p \land p)$

$\equiv (\sim p \land \sim q) \lor c$

$\equiv (\sim p \land \sim q)$

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