JEE Main202312 Apr 2023Morning ShiftMathematicsMathematical ReasoningActual
Among the two statements S 1 : p ⇒ q ∧ p ∧ ~ q is a contradiction and S 2 : p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ∨ ~ p ∧ ~ q is a tautology
Options
- Aonly ( S 2 ) is true
- Bonly ( S 1 ) is true
- Cboth are false
- Dboth are true
Correct answer
D. both are true
Step-by-step solution
Given, S 1 : p ⇒ q ∧ p ∧ ~ q ≡ ~ p ∨ q ∧ p ∧ ~ q as   A ⇒ B ≡ ~ A ∨ B ≡ ~ p ∧ p ∧ ~ q ∨ q ∧ p ∧ ~ q ≡ f ∧ ~ q ∨ f ∧ p ≡ f ∨ f ≡ f S 2 : p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ∨ ~ p ∧ ~ q ≡ p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ∨ ~ p ∧ ~ q ≡ p ∨ ~ p ∧ q ∨ p ∨ ~ p ∧ ~ q ≡