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JEE Main202126 Aug 2021Morning ShiftMathematicsMathematical ReasoningActual

If the truth value of the Boolean expression ( ( p ∨ q ) ∧ ( q → r ) ∧ ( ~ r ) ) → ( p ∧ q ) is false, then the truth values of the statements p , q , r respectively can be:

Options

  1. AFTF
  2. BTFF
  3. CTFT
  4. DFFT

Correct answer

B. TFF

Step-by-step solution

p q r p ∨ q q → r ~ r ( p ∨ q ) ∧ ( q → r ) ∧ ~ r p ∧ q ( ( p ∨ q ) ∧ ( q → r ) ∧ ~ r ) → p ∧ q  T  T T T T F F T T T T F T F T F T T T F T T T F F F T T F F T T T T F F F T T T T F F F T F T F T F T F F T F F T F T F F F T F F F F T T F F T

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