JEE Main20236 Apr 2023Evening ShiftMathematicsMathematical ReasoningActual
Among the statements S 1 : p ⇒ q ∨ ~ p ∧ q is a tautology S 2 : q ⇒ p ⇒ ~ p ∧ q is a contradiction
Options
- ANeither S 1 and S 2 is True
- BBoth S 1 and S 2 are True
- COnly S 2 is True
- DOnly S 1 is True
Correct answer
A. Neither S 1 and S 2 is True
Step-by-step solution
Plotting the Truth table of the given expression we get, p q ~ p ~ p ∧ q p ⇒ q q ⇒ p p ⇒ q ∨ ~ p ∧ q q ⇒ p ∨ ~ p ∧ q T T F F T T T T T F F F F T F T F T T T T F T T F F T F T T T T Hence, q ⇒ p ∨ ~ p ∧ q is a tautology, and p ⇒ q ∨ ~ p ∧ q is neither tautology and contradiction, So both statements are false.