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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 equivalent to

The statement p→(q→p)isequivalenttop \to \left(q \to p\right) is equivalent to

Options

  1. Ap→(p→q)p \to \left(p \to q\right)
  2. Bp→(p∨q)p \to \left(p ∨ q\right)
  3. Cq→pq \to p
  4. Dq→(p→q)q \to \left(p \to q\right)

Correct answer

C. q→pq \to p

Step-by-step solution

∵s→r≡s∨r∵ s \to r ≡ s ∨ r
∴p→(q→p)≡p∨(q→p)∴ p \to \left(q \to p\right) ≡ p ∨ \left(q \to p\right)
≡p∨(q∨p)≡q∨p=q→p≡ p ∨ \left( q ∨ p\right) ≡ q ∨ p = q \to p
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