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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

The compound statement (p ↔ q) ∨ (p ↔ q) is logically equivalent to

The compound statement (p↔q)∨(p↔q)\left(p ↔ q\right) ∨ \left(p ↔ q\right) is logically equivalent to$$

Options

  1. Ap↔qp ↔ q
  2. Bp∨qp ∨ q
  3. Ctautology
  4. Dcontradiction

Correct answer

C. tautology

Step-by-step solution

We know that  (p↔q)≡p↔ q~ \left(p ↔ q\right) ≡ p ↔ ~ q
∴∴ given statement is \left(p ↔ q\right) ∨ \left\{~ \left(p ↔ q\right)\right\}<br/>whichisatautology{∵p∨( p)≡t}<br />which is a tautology \left\{∵ p ∨ \left(~ p\right) ≡ t\right\}
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