NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice
If p and q are logical statements, then p ∧ q → p → q is equivalent to
Options
- Ap ∧ q
- Bp → p ∨ q
- Cp ∨ q
- Dp ∨ q ⟷ p ∧ q
Correct answer
B. p → p ∨ q
Step-by-step solution
∵ s → t ≡ ~ s ∨ t ∴ p ∧ q → p → q ≡ ∼ p ∨ ∼ q ∨ ~ p ∨ q ≡ ~ p ∨ q ∨ ~ q ≡ ∼ p ∨ t ≡ t Also, p → p ∨ q ≡ ~ p ∨ p ∨ q ≡ t