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JEE Main202331 Jan 2023Morning ShiftMathematicsMathematical ReasoningActual

Consider: S 1 : p ⇒ q ∨ p ∧ ~ q is a tautology. S 2 : ~ p ⇒ ~ q ∧ ~ p ∨ q is a contradiction. Then

Options

  1. Aonly S 2 is correct
  2. Bboth S 1 and S 2 are correct
  3. Cboth S 1 and S 2 are wrong
  4. Donly S 1 is correct

Correct answer

D. only S 1 is correct

Step-by-step solution

p q p ⇒ q ~ q p ∧ ~ q p ⇒ q ∨ p ∧ ~ q T T T F F T T F F T T T F T T F F T F F T T F T So, p ⇒ q ∨ p ∧ ~ q is a tautology. ~ p ~ q ~ p ⇒ ~ q ~ p ∨ q ~ p ⇒ ~ q ∧ ~ p ∨ q F F T T T F T T F F T F F T F T T T T T

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