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JEE Main20205 Sep 2020Morning ShiftMathematicsMathematical ReasoningActual

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

Options

  1. A( ~ x ∧ y ) ∨ ( ~ x ∧ ~ y )
  2. B( x ∧ y ) ∨ ( ~ x ∧ ~ y )
  3. C( x ∧ ~ y ) ∨ ( ~ x ∧ y )
  4. D( x ∧ y ) ∧ ( ~ x ∨ ~ y )

Correct answer

B. ( x ∧ y ) ∨ ( ~ x ∧ ~ y )

Step-by-step solution

Negation of x ↔ ~ y ≡ ~ x ↔ ~ y ≡ ~ x → ~ y ∧ ~ y → x ≡ ~ x → ~ y ∨ ~ ~ y → x (using De'Morgan's laws) ≡ x ∧ y ∨ ~ y ∧ ~ x

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