MHT CET2017MathematicsMathematical Reasoning
Which of the following statement pattern is a tautology?
Options
- Ap ∨ ( q → p )
- B∽ q → ∽ p
- Cq → p ∨ ∽ p ↔ q
- Dp ∧ ∽ p
Correct answer
C. q → p ∨ ∽ p ↔ q
Step-by-step solution
It can be done using truth or using rules of logic. (i) p ∨ q → p ≡ p ∨ ∽ q ∨ p ≡ p ∨ p ∨ ∽ q ≡ p ∨ ∽ q (ii) ∽ q → ∽ p ≡ q ∨ ∽ p (iv) p ∧ ∽ p ≡ F So left is (iii) p q q → p ∽ p ∽ p ↔ q q → p ∨ ∽ p ↔ q T T T F F T T F T F T T F T F T T T F F T T F T