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JEE Main202329 Jan 2023Morning ShiftMathematicsMathematical ReasoningActual

If p , q and r are three propositions, then which of the following combination of truth values of p , q and r makes the logical expression ( p ∨ q ) ∧ ( ( ~ p ) ∨ r ) → ( ( ~ q ) ∨ r ) false ?

Options

  1. Ap = T , q = F , r = T
  2. Bp = T , q = T , r = F
  3. Cp = F , q = T , r = F
  4. Dp = T , q = F , r = F

Correct answer

C. p = F , q = T , r = F

Step-by-step solution

Given, ( p ∨ q ) ∧ ( ( ~ p ) ∨ r ) → ( ( ~ q ) ∨ r ) Now solving the above expression using truth table from given options we get, p q r p ∨ q ~ p ∨ r A ≡ p ∨ q ∧ ~ p ∨ r B ≡ ~ q ∨ r A → B A T F T T T T T T B T T F T F F F T C F T F T T T F F D T F F T F F T T So, only Option C will be false.

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