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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 statements is not a fallacy?

Which of the following 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. Dp∨(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 Aistrueonlyifis true only ifpis true and \left( p ⇒ q\right) is false which is never possible hence \left(A\right) is a fallacy
\left(B\right)\left(p ∧ q\right) is a subset of pp hence \left(p ∧ q\right)⇒pis a tautology hence \left(\left(p ∧ q\right)⇒ p\right)is a fallacy
\left(C\right) pis subsetof(p∨q)henceof \left(p ∨ q\right) hencep ⇒ \left(p ∨ q\right)is tautology hence \left(p ⇒\left(p ∨ q\right)\right)is a fallacy
\left(D\right) Option \left(D\right) isthethenegation of option \left(A\right) hence \left(D\right) is a tautology
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