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JEE Main 202124 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2021 · 24 February · Evening Shift · Mathematics · Mathematical Reasoning

The negation of the statement ~ p ∧ (p ∨ q) is:

The negation of the statement  p∧(p∨q)~ p ∧ \left(p ∨ q\right) is:

Options

  1. A p∨q~ p ∨ q
  2. B p∧q~ p ∧ q
  3. Cp∨ qp ∨ ~ q
  4. Dp∧ qp ∧ ~ q

Correct answer

C. p∨ qp ∨ ~ q

Step-by-step solution

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

p∨( p∧ q)p ∨ \left(~ p ∧ ~ q\right)

(p∨ p)⏟t∧(p∨ q)\mathop{\mathop{\left(p ∨ ~ p\right)}_{⏟}}_{t} ∧ \left(p ∨ ~ q\right)

P∨ qP ∨ ~ q

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