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JEE Main202225 Jun 2022Evening ShiftMathematicsMathematical ReasoningActual

The negation of the Boolean expression ~ q ∧ p ⇒ ~ p ∨ q is logically equivalent to

Options

  1. Ap ⇒ q
  2. Bq ⇒ p
  3. C~ p ⇒ q
  4. D~ q ⇒ p

Correct answer

C. ~ p ⇒ q

Step-by-step solution

To find negation of ( ~ q ∧ p → ~ p ∨ q Let ~ q ∧ p = A & ~ p ∨ q = B ~ A → B = ~ ~ A ∨ B = A ∧ ~ B Using above formula be get ~ q ∧ p ∧ ~ ~ p ∨ q = ~ q ∧ p ∧ p ∧ ~ q = A ∧ A = A = ~ q ∧ p = p ∧ ~ q or ~ p → q

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