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NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice

If p and q are two statements, then p ∨ ∼ p ⇒   ∼ q is equivalent to

Options

  1. Ap ∧ q
  2. Bp
  3. Cp ∧ ∼ q
  4. D∼ p ∧ q

Correct answer

B. p

Step-by-step solution

As we know that p → q ≡ ∼ p ∨ q Hence p ∨ ∼ p → ∼ q ≡ p ∨ ∼ ∼ p ∨ ∼ q as we know that ~ p ∨ q ≡ ~ p ∧ ~ q Hence p ∨ ∼ ∼ p ∨ ∼ q ≡ p ∨ p ∧ q Therefore p ∨ p ∧ q ≡ p

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