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JEE Main20231 Feb 2023Morning ShiftMathematicsMathematical ReasoningActual

The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to

Options

  1. A( ~ p ) ∧ ( ~ q )
  2. Bp ∧ ( ~ q )
  3. C( ~ p ) ∨ ( ~ q )
  4. D( ~ p ) ∨ q

Correct answer

A. ( ~ p ) ∧ ( ~ q )

Step-by-step solution

The negation of q ∨ ( ( ~ q ) ∧ p ) is ~ ( q ∨ ( ( ~ q ) ∧ p ) ) ≡ ~ q ∧ ~ ( ( ~ q ) ∧ p ) ≡ ~ q ∧ ( q ∨ ~ p ) ≡ ( ~ q ∧ q ) ∨ ( ~ q ∧ ~ p ) ≡ ( ~ q ∧ ~ p )

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