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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2019 · 12 January · Morning Shift · Mathematics · Mathematical Reasoning

The Boolean expression ((p ∧ q) ∨ (p ∨ ~ q)) ∧ (~ p ∧ ~ q) is...

The Boolean expression ((p∧q)∨(p∨ q))∧( p∧ q)isequivalentto\left(\left(p ∧ q\right) ∨ \left(p ∨ ~ q\right)\right) ∧ \left(~ p ∧ ~ q\right) is equivalent toThe Boolean expression ((p ∧ q) ∨ (p ∨ ~ q)) ∧ (~ p ∧ ~ q) is equivalent to

Options

  1. Ap∧( q)p ∧ \left(~ q\right)
  2. B( p)∧( q)\left(~ p\right) ∧ \left(~ q\right)
  3. Cp∨( q)p ∨ \left(~ q\right)
  4. Dp∧qp ∧ q

Correct answer

B. ( p)∧( q)\left(~ p\right) ∧ \left(~ q\right)

Step-by-step solution

The Boolean expression ((p ∧ q) ∨ (p ∨ ~ q)) ∧ (~ p ∧ ~ q) is equivalent to

p∧q≡bp ∧ q ≡ b

p∨ q≡a+b+dp ∨ ~ q ≡ a + b + d

 p∧ q≡d~ p ∧ ~ q ≡ d

∴(p∧q)∨(p∨ q)≡a+b+d∴ \left(p ∧ q\right) ∨ \left(p ∨ ~ q\right) ≡ a + b + d

\left(\left(p ∧ q\right) ∨ \left(p ∨ ~ q\right)\right) ∧ \left(~ p ∧ ~ q\right) ≡ d ≡ \left(~ p\right) ∧ \left(~ q\right)

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