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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If p and q are two statements, then p ∨ ∼ (p ⇒ ∼ q) is equivalent to

If pp and qq are two statements, then p∨∼(p⇒∼q)isequivalenttop ∨ ∼ \left(p ⇒ ∼ q\right) is equivalent to

Options

  1. Ap∧qp ∧ q
  2. Bpp
  3. Cp∧∼qp ∧ ∼ q
  4. D∼p∧q∼ p ∧ q

Correct answer

B. pp

Step-by-step solution

As we know that p→q≡∼p∨qp \to q ≡ ∼ p ∨ q

Hence p∨∼(p→∼q)≡p∨∼(∼p∨∼q)p ∨ ∼ \left(p \to ∼ q\right) ≡p ∨ ∼ \left(∼ p ∨ ∼ q\right)

as we know that (p∨q)≡p∧q\left(p ∨ q\right) ≡ p ∧ q

Hence p∨∼(∼p∨∼q)≡p∨(p∧q)p ∨ ∼ \left(∼ p ∨ ∼ q\right) ≡ p ∨ \left(p ∧ q\right)

Therefore p∨(p∧q)≡pp ∨ \left(p ∧ q\right) ≡ p
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