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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 statements is not a fallacy?

Which of the statements is not a fallacy?

Options

  1. Ap∧(∼(∼p⇒∼q))p ∧ \left(∼ \left(∼ p ⇒ ∼ q\right)\right)
  2. B∼((p∧∼q)⇒p)∼ \left( \left(p ∧ ∼ q\right) ⇒ p\right)
  3. C∼(p⇒(p∨∼q))∼ \left(p ⇒ \left(p ∨ ∼ q\right)\right)
  4. D∼p∨(∼p⇒∼q)∼ p ∨ \left(∼ p ⇒ ∼ q\right)

Correct answer

D. ∼p∨(∼p⇒∼q)∼ p ∨ \left(∼ p ⇒ ∼ q\right)

Step-by-step solution

(A)\left(A\right) Option (A)\left(A\right) is true only if pp is true and (∼p⇒∼q)\left(∼ p ⇒ ∼ q\right) is false which can never be possible, hence (A)\left(A\right) is a fallacy
∴s→t∴ s \to t is a tautology, if ss is subset of tt
(B)\left(B\right)\left(p ∧ ∼ q\right)isasubsetofis a subset ofp,hence(p∧∼q)hence \left(p ∧ ∼ q\right)⇒ pisatautology,henceis a tautology, hence∼ \left((p∧∼q)\left(p ∧ ∼ q\right)⇒ p\right)isafallacy<br/>is a fallacy<br />\left(C\right)pp is a subset of (p∨q)\left(p ∨ q\right), hence p⇒(p∨∼q)p ⇒ \left(p ∨ ∼ q\right) is a tautology, hence ∼∼\left(p ⇒ \left(p ∨ ∼ q\right)\right)isafallacy<br/>is a fallacy<br />\left(D\right)OptionOption\left(D\right)isthenegationofoptionis the negation of option\left(A\right),hence(D), hence \left(D\right) is a tautology
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