MHT CET2019Evening ShiftMathematicsMathematical ReasoningActual
Which of the following statement is contingency?
Options
- Ap ∨ q ∨ ∼ q
- Bp ∨ q ∨ ∼ p
- Cp ∨ q ∧ ∼ q
- Dp → p ∨ q
Correct answer
C. p ∨ q ∧ ∼ q
Step-by-step solution
Key Idea : A statement which is neither a tautology nor a contradiction is a contingency. Option (1) p ∨ q ∨ ∼ q ≡ p ∨ q ∨ ∼ q ≡ p ∨ T ≡ T which is a tautology. Option (2) p ∨ q ∨ ∼ ≡ p ∨ q ∨ ∼ ≡ p ∨ ∼ q ∨ q ≡ T ∨ q ≡ T which is tautology Option (3) p ∨ q ∧ ∼ q ≡ p ∧ ∼ q ∨ q ∧ ∼ q ≡ p ∧ ∼ q ∨ F ≡ p ∧ ∼ q If p → T , q → T Then p ∧ ∼ q → F If p → T , q → F Then p ∧ ∼ q → T So, p ∧ ∼ q is a contingency. Therefore statement p ∨ q ∧ ∼ q is contingency.