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JEE Main201910 Apr 2019Morning ShiftMathematicsMathematical ReasoningActual

Which one of the following Boolean expression is a tautology?

Options

  1. Ap ∨ q ∧ ~ p ∨ ~ q
  2. Bp ∧ q ∨ p ∧ ~ q
  3. Cp ∨ q ∧ p ∨ ~ q
  4. Dp ∨ q ∨ ~ p ∨ ~ q

Correct answer

D. p ∨ q ∨ ~ p ∨ ~ q

Step-by-step solution

Let I = p ∨ q ∨ p ∨ ~ q I I =   p ∧ q ∨ p ∧ ~ q I I I =   p ∨ q ∧ p ∨ ~ q   I V =   p ∨ q ∧ ~ p ∨ ~ q p q p ∨ q p ∧ q ∼ p ∼ q p ∨ ∼ q p ∧ ∼ q I I I I I I I V T T T T F F T F T T T F T F T F F T T T T T T T F T T F T F F F T F F T F F F F T T T F T F F F

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