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JEE Main202325 Jan 2023Evening ShiftMathematicsMathematical ReasoningActual

Let △ , ∇ ∈ ∧ , ∨ be such that ( p → q ) △ ( p ∇ q ) is a tautology. Then

Options

  1. A△ = ∧ , ∇ = ∨
  2. B△ = ∨ , ∇ = ∧
  3. C△ = ∨ , ∇ = ∨
  4. D△ = ∧ , ∇ = ∧

Correct answer

C. △ = ∨ , ∇ = ∨

Step-by-step solution

Given, △ , ∇ ∈ ∧ , ∨ be such that ( p → q ) △ ( p ∇ q ) is a tautology Now checking all options by making truth table we get, Option A △ = ∧ , ∇ = ∨ p q ( p → q ) ( p ∨ q ) ( p → q ) ∧ ( p ∨ q ) T T T T T T F F T F F T T T T F F T F F Option B △ = ∨ , ∇ = ∧ p q ( p → q ) ( p ∧ q ) ( p → q ) ∨ ( p ∧ q ) T T T T T T F F F F F T T F T F F T F T Option C △ = &

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