Verified Solution • 2025–26 Session moderate

QJEEM20Mabbd1: JEE Main 2020 Mathematics - Class 11 JEEM20Mabbd1 Solution: The negation of the Boolean expression x ~ y is equivalent to :

The negation of the Boolean expression x ↔\leftrightarrow ~ y is equivalent to :

Multiple Choice Options

  • A (x∧y)∨(∼x∧∼y)\left( {x \wedge y} \right) \vee \left( { \sim x \wedge \sim y} \right)
  • B (∼x∧y)∨(∼x∧∼y)\left( { \sim x \wedge y} \right) \vee \left( { \sim x \wedge \sim y} \right)
  • C (x∧y)∧(∼x∨∼y)\left( {x \wedge y} \right) \wedge \left( { \sim x \vee \sim y} \right)
  • D (x∧∼y)∨(∼x∧y)\left( {x \wedge \sim y} \right) \vee \left( { \sim x \wedge y} \right)

Step-by-Step Verified Solution

We know, p ↔\leftrightarrow q ≡\equiv (p→q)∧(q→p)\left( {p \to q} \right) \wedge \left( {q \to p} \right)

∴\therefore x ↔\leftrightarrow ~ y ≡\equiv (x→∼y)∧(∼y→x)\left( {x \to \sim y} \right) \wedge \left( { \sim y \to x} \right)

[ Also p→q≡∼p∨qp \to q \equiv \sim p \vee q ]

⇒\Rightarrow x ↔\leftrightarrow ~ y ≡\equiv (∼x∨∼y)∧(y∨x)\left( { \sim x \vee \sim y} \right) \wedge \left( {y \vee x} \right)

∴\therefore ∼(x↔∼y)≡(x∧y)∨(∼y∧∼x)\sim \left( {x \leftrightarrow \sim y} \right) \equiv \left( {x \wedge y} \right) \vee \left( { \sim y \wedge \sim x} \right)

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