NTA Abhyas JEE Main2020MathematicsMathematical ReasoningPractice
If p and q are two statements, then p ∨ ∼ p ⇒   ∼ q is equivalent to
Options
- Ap ∧ q
- Bp
- Cp ∧ ∼ q
- D∼ p ∧ q
Correct answer
B. p
Step-by-step solution
As we know that p → q ≡ ∼ p ∨ q Hence p ∨ ∼ p → ∼ q ≡ p ∨ ∼ ∼ p ∨ ∼ q as we know that ~ p ∨ q ≡ ~ p ∧ ~ q Hence p ∨ ∼ ∼ p ∨ ∼ q ≡ p ∨ p ∧ q Therefore p ∨ p ∧ q ≡ p