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JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Mathematical Reasoning

The Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to

The Boolean expression ∼∼\left(p ⇒ \left(∼ q\right)\right) is equivalent to

Options

  1. A(∼p)⇒q( ∼ p ) ⇒ q
  2. Bq⇒∼pq ⇒ ∼ p
  3. Cp∨qp ∨ q
  4. Dp∧qp ∧ q

Correct answer

D. p∧qp ∧ q

Step-by-step solution

Recall p⇒q≡ p∨qp ⇒ q ≡ ~ p ∨ q

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

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