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JEE Main202311 Apr 2023Evening ShiftMathematicsMathematical ReasoningActual

The converse of ~ p ∧ q ⇒ r is

Options

  1. A~ p ∨ q ⇒ r
  2. B~ r ⇒ p ∧ q
  3. C~ r ⇒ ~ p ∧ q
  4. Dp ∨ ~ q ⇒ ~ r

Correct answer

D. p ∨ ~ q ⇒ ~ r

Step-by-step solution

We know that, Converse of A ⇒ B is B ⇒ A So, using the above formula we get, Converse of ~ p ∧ q ⇒ r ≡ r ⇒ ( ~ p ∧ q ) ≡ ~ r ∨ ~ p ∧ q ≡ ~ p ∧ q ∨ ~ r ≡ ~ p ∨ ~ q ∨ ~ r   as   ~ A ∨ B ≡ ~ A ∧ ~ B ≡ p ∨ ~ q ⇒ ~ r

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