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JEE Main202227 Jul 2022Morning ShiftMathematicsMathematical ReasoningActual

p ∧ r ⇔ p ∧ ~ q is equivalent to ~ p when r is

Options

  1. Ap
  2. B~ p
  3. Cq
  4. D~ q

Correct answer

C. q

Step-by-step solution

Given p ∧ r ⇔ p ∧ ~ q ≡ ~ p Assuming all option one by one, Taking r = p p q ~ p ~ q p ∧ p p ∧ ~ q p ∧ r ⇔ p ∧ ~ q T T F F T F F T F F T T T T F T T F F F T F F T T F F T Now taking r = ~ p p q ~ p ~ q p ∧ ~ p p ∧ ~ q p ∧ r ⇔ p ∧ ~ q T T F F F F T T F F T F T F F T T F F F T F F T T F F T Taking r = q p q ~ p ~ q p ∧ q p ∧ ~ q p ∧ r ⇔ p ∧ ~ q T T F F T F F T F F T F T F F T T F F F T F F T T F F T So cl

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