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JEE Main202229 Jul 2022Evening ShiftMathematicsMathematical ReasoningActual

The statement p ⇒ q ∨ p ⇒ r is NOT equivalent to:

Options

  1. Ap ∧ ~ r ⇒ q
  2. B~ q ⇒ ~ r ∨ p
  3. Cp ⇒ q ∨ r
  4. Dp ∧ ~ q ⇒ r

Correct answer

B. ~ q ⇒ ~ r ∨ p

Step-by-step solution

Given, p ⇒ q ∨ p ⇒ r Now using the formula A ⇒ B ≡ ~ A ∨ B We get, ~ p ∨ q ∨ ~ p ∨ r ≡ ~ p ∨ q ∨ r ≡ p ⇒ q ∨ r , so option C is true. Now solving option 1 we get, p ∧ ~ r ⇒ q ≡ ~ p ∧ ~ r ∨ q ≡ ~ p ∨ r ∨ q ≡ ~ p ∨ r ∨ q ≡ ~ p ∨ r ∨ ~ p ∨ q ≡ p ⇒ q ∨ p ⇒ r , so option 1 is also true, Now solving option 4 we get, p &#

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