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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

Which of the following option is incorrect?

Which of the following option is incorrect?

Options

  1. A (p⇔ q)≡p⇔q~ \left(p ⇔ ~ q\right) ≡ p ⇔ q
  2. B(p⇔q)≡(p→q)∧(q→p)\left(p ⇔ q\right) ≡ \left(p \to q\right) ∧ \left( q \to p\right)
  3. C (p⇔q)≡ p⇒q~ \left(p ⇔ q\right) ≡ ~ p ⇒ q
  4. D (p⇒q)≡p∧∼q~ \left(p ⇒ q\right) ≡ p ∧ ∼ q

Correct answer

C.  (p⇔q)≡ p⇒q~ \left(p ⇔ q\right) ≡ ~ p ⇒ q

Step-by-step solution

Option (D) is a theorem, hence (D) is correct
For option (B), s↔t≡(s→t)∧(t→s)s ↔ t ≡ \left(s \to t\right) ∧ \left(t \to s\right), hence (B) is correct
For option (A), (p⇔q)≡p⇔(q)\left(p ⇔ q\right) ≡ p ⇔ \left( q\right)
≡p⟺q≡ p ⟺ q
Hence, (A) is correct
For option (C), (p⇔q)≡p⇔q\left(p ⇔ q\right) ≡ p ⇔ q
Hence, option (C) is incorrect
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