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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2016 · 3 April · Mathematics · Mathematical Reasoning

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

The Boolean Expression (p∧∼q)∨q∨(∼p∧q)isequivalentto\left(p ∧ ∼ q\right) ∨ q ∨ \left(∼ p ∧ q\right) is equivalent to

Options

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

Correct answer

A. p∨qp ∨ q

Step-by-step solution

\left(p ∧ ∼ q\right) ∨ q ∨ \left(∼ p ∧ q\right)

Set equivalent

=(A∩B−)= \left(A \cap \overset{-}{B}\right) \cup \left(\overset{-}{A} \cap B\right)∪B\cup B

=((A∪B)= ( \left(A \cup B\right) - \left(A \cap B)\right)∪B\cup B

=A∪B= A \cup B

Hence answer is p∨qp ∨ q .
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