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JEE Main 202227 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2022 · 27 June · Morning Shift · Mathematics · Mathematical Reasoning

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

The boolean expression ( (p∧q))∨q\left(~ \left(p ∧ q\right)\right) ∨ q is equivalent to

Options

  1. Aq→(p∧q)q \to \left(p ∧ q\right)
  2. Bp→qp \to q
  3. Cp→(p→q)p \to \left(p \to q\right)
  4. Dp→(p∨q)p \to \left(p ∨ q\right)

Correct answer

D. p→(p∨q)p \to \left(p ∨ q\right)

Step-by-step solution

Given  (p∧q)∨q≡ p∨ q∨q≡ p∨t≡t~ \left(p ∧ q\right) ∨ q ≡ ~ p ∨ ~ q ∨ q ≡ ~ p ∨ t ≡ t

Also p→(p∨q)≡ p∨(p∨q)≡ p∨p∨q≡t∨q≡tp \to \left(p ∨ q\right) ≡ ~ p ∨ \left(p ∨ q\right) ≡ ~ p ∨ p ∨ q ≡ t ∨ q ≡ t

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