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JEE Main202226 Jun 2022Evening ShiftMathematicsMathematical ReasoningActual

Let r ∈ P , q , ~ p , ~ q be such that the logical statement r ∨ ~ p ⇒ p ∧ q ∨ r is a tautology. Then r is equal to

Options

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

Correct answer

C. ~ p

Step-by-step solution

Solving all option one by one we get following truth table, (1) p = r q ~ p r ∨ ~ p p ∧ q p ∧ q ∨ r r ∨ ~ p ⇒ p ∧ q ∨ r T F F T F T T F T T T F F F T T F T T T T F F T T F F T (2) p ~ p r ∨ ~ p q = r p ∧ q p ∧ q ∨ r r ∨ ~ p ⇒ p ∧ q ∨ r T F T T T T T F T T T F T T T F F F F F T F T T F F F F (3) p q r = ~ p r ∨ ~ p p ∧ q p ∧ q ∨ r r ∨ ~ p ⇒ p ∧ q ∨ r T T F F T T T F T T T F

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