Verified Solution • 2025–26 Session moderate

QJEEM21Ma7b79: JEE Main 2021 Mathematics - Class 11 JEEM21Ma7b79 Solution: The Boolean expression is equivalent to :

The Boolean expression (p⇒q)∧(q⇒∼p)(p \Rightarrow q) \wedge (q \Rightarrow \sim p) is equivalent to :

Multiple Choice Options

  • A ∼\sim q
  • B q
  • C p
  • D ∼\sim p

Step-by-Step Verified Solution

(p→q)∧(q→∼p)(p \to q) \wedge (q \to \sim p)

≡(∼p∨q)∧(∼q∨∼p){p→q≡∼p∨q}\equiv ( \sim p \vee q) \wedge ( \sim q \vee \sim p)\{ p \to q \equiv \sim p \vee q\}

≡(∼p∨q)∧(∼p∨q)\equiv ( \sim p \vee q) \wedge ( \sim p \vee q) {commutative property}

≡∼p∨(q∧∼q)\equiv \sim p \vee (q \wedge \sim q) {distributive property}

≡∼p\equiv \sim p

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