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JEE Main202225 Jul 2022Morning ShiftMathematicsMathematical ReasoningActual

Which of the following statements is a tautology?

Options

  1. A~ p ∨ q ⇒ p
  2. Bp ⇒ ~ p ∨ q
  3. C~ p ∨ q ⇒ q
  4. Dq ⇒ ~ p ∨ q

Correct answer

D. q ⇒ ~ p ∨ q

Step-by-step solution

Plotting the truth table of the following option we have, p q ~ p ~ q ~ p ∨ q T T F F T T F F T F F T T F T F F T T T We know that, A ⇒ B is only false when A is true and B is false, now using this rule and above table we will make truth table of options, ~ p ∨ q ⇒ p p ⇒ ~ p ∨ q ~ p ∨ q ⇒ q q ⇒ ~ p ∨ q T T T T T F T T F T T T F T F T Hence q ⇒ ~ p ∨ q is tautology.

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