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JEE Main202124 Feb 2021Evening ShiftMathematicsMathematical ReasoningActual

For the statements p and q , consider the following compound statements: a   ~ q ∧ p → q → ~ p b   p ∨ q ∧ ~ p → q Then which of the following statements is correct?

Options

  1. Ab is a tautology but not a .
  2. Ba and b both are tautologies.
  3. Ca and b both are not tautologies.
  4. Da is a tautology but not b .

Correct answer

B. a and b both are tautologies.

Step-by-step solution

p q ~ q p → q ~ p ~ q ∧ p → q T T F T F F T T F T F F F T F T F T T F T F F T T T T T p q p ∨ q ~ p p ∨ q ∧ ~ p T T T F F T T F T F F T F T T T T T F F F T F T Both are tautologies

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