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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

The statement p ⇒ (q ∧ p) is negation of the statement

The statement p⇒(q∧p)isnegationofthestatementp ⇒ \left(q ∧ p\right) is negation of the statement

Options

  1. Ap⇒qp ⇒ q
  2. Bp∧qp ∧ q
  3. C(p⇒q)\left(p ⇒ q\right)
  4. D(p∧q)\left(p ∧ q\right)

Correct answer

C. (p⇒q)\left(p ⇒ q\right)

Step-by-step solution

∵ \left(s ⇒ t\right) ≡ s ∧ \left( t\right)<br/><br />∵ \left(p ⇒ \left(q ∧ p\right)\right) ≡ p ∧ \left( \left(q ∧ p\right)\right)<br/><br />≡ p ∧ \left( q ∨ p\right)<br/><br />≡ \left(p ∧ q\right) ∨ \left(p ∧ p\right)<br/><br />≡ \left(p ∧ p\right) ∨ f<br/><br />≡ p ∧ q ≡ \left(p ⇒ q\right)
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