NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice
Which of the following statements is not a fallacy?
Options
- Ap ∧ ~ ~ p ⇒ q
- B~ p ∧ q ⇒ p
- C~ p ⇒ p ∨ q
- D~ p ∨ ~ p ⇒ q
Correct answer
D. ~ p ∨ ~ p ⇒ q
Step-by-step solution
A Option A is true only if p is true and ~ p ⇒ q is false which is never possible hence A is a fallacy B p ∧ q is a subset of p hence p ∧ q ⇒ p is a tautology hence ~ p ∧ q ⇒ p is a fallacy C p is subset of p ∨ q hence p ⇒ p ∨ q is tautology hence ~ p ⇒ p ∨ q is a fallacy D Option D is the negation of option A hence D is a tautology