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NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice

∼ p ∨ q ∨ ∼ p ∧ q is equivalent to

Options

  1. Ap
  2. B∼ p
  3. Cq
  4. D∼ q

Correct answer

B. ∼ p

Step-by-step solution

~ p ∨ q ∨ ~ p ∧ q ≡ ~ p ∧ ~ q ∨ ~ p ∧ q (By De morgan's Law) ≡ ∼ p ∧ ∼ q ∨ q (By complement laws) ≡ ~ p ∧ t (By Identity Laws) ≡ ~ p

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