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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 logical statements, then ( p)→ (p → q) is equivalent...

If pandqp and q are logical statements, then \left( p\right)\to \left(p \to q\right) is equivalent to

Options

  1. Ap∧qp ∧ q
  2. Bp→(p∨q)p \to \left(p ∨ q\right)
  3. Cp∨qp ∨ q
  4. D(p∨q)↔(p∧q)\left(p ∨ q\right) ↔ \left(p ∧ q\right)

Correct answer

B. p→(p∨q)p \to \left(p ∨ q\right)

Step-by-step solution

∴s→t≡∼s∨t∴ s \to t ≡ ∼ s ∨ t
∴(p)→(p→q)≡(p)∨(p→q)∴ \left( p\right) \to \left(p \to q\right) ≡ \left(p\right) ∨ \left(p \to q\right)
≡(p)∨(∼p∨q)≡ \left(p\right) ∨ \left(∼ p ∨ q\right)
≡(p∨∼p)∨q≡ \left(p ∨ ∼ p\right) ∨ q
≡t∨q≡t≡ t ∨ q ≡ t
Also, p→(p∨q)≡∼p∨(p∨q)≡tp \to \left(p ∨ q\right) ≡ ∼ p ∨ \left(p ∨ q\right) ≡ t
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