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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Mathematical Reasoning

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

The negation of the Boolean expression p∨( p∧q)p ∨ ( ~ p ∧ q ) is equivalent to :

Options

  1. Ap∧ qp ∧ ~ q
  2. B p∧ q~ p ∧ ~ q
  3. C p∨ q~ p ∨ ~ q
  4. D p∨q~ p ∨ q

Correct answer

B.  p∧ q~ p ∧ ~ q

Step-by-step solution

Given statement is p∨(q∧ p)p ∨ ( q ∧ ~ p )
∴∴ Negation is  (p∨(q∧ p))~ ( p ∨ ( q ∧ ~ p ) )
=( p∧ q)∨( p∧p)= ( ~ p ∧ ~ q ) ∨ ( ~ p ∧ p )
=( p∧ q)∨c= ( ~ p ∧ ~ q ) ∨ c
= p∧ q= ~ p ∧ ~ q
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