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JEE Main2016MathematicsMathematical ReasoningActual

The Boolean Expression p ∧ ∼ q ∨ q ∨ ∼ p ∧ q is equivalent to

Options

  1. Ap ∨ q
  2. Bp ∨ ∼ q
  3. C∼ p ∧ q
  4. Dp ∧ q

Correct answer

A. p ∨ q

Step-by-step solution

p ∧ ∼ q ∨ q ∨ ∼ p ∧ q Set equivalent = A ∩ B - ∪ A - ∩ B ∪ B = ( A ∪ B - A ∩ B) ∪ B = A ∪ B Hence answer is p ∨ q .

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