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JEE Main20199 Jan 2019Evening ShiftMathematicsMathematical ReasoningActual

The logical statement ~ ~ p ∨ q ∨ p ∧ r ∧ ~ q ∧ r is equivalent to

Options

  1. A~ p ∧ ~ q ∧ r
  2. Bp ∧ r ∧ ~ q
  3. Cp ∧ ~ q ∨ r
  4. D~ p ∨ r

Correct answer

B. p ∧ r ∧ ~ q

Step-by-step solution

~ ~ p ∨ q ∨ p ∧ r ∧ ~ q ∧ r = p ∧ ~ q ∨ p ∧ r ∧ ~ q ∧ r By distributive law = p ∧ ~ q ∨ r ∧ ~ q ∧ r p ∧ ~ q ∧ r ≡ p ∧ r ∧ ~ q = p ∧ ∼ q ∧ r By Associative law = p ∧ r ∧ ~ q

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