JEE Main202310 Apr 2023Evening ShiftMathematicsMathematical ReasoningActual
The statement ~ p ∨ ~ p ∧ q is equivalent to
Options
- A~ p ∧ q
- Bp ∧ q ∧ ~ p
- C~ p ∧ q ∧ q
- D~ p ∨ q
Correct answer
B. p ∧ q ∧ ~ p
Step-by-step solution
Given, ~ p ∨ ~ p ∧ q Now we know that, By demorgan law, ~ A ∨ B ≡ ~ A ∧ ~ B Now using above formula we get, ~ p ∨ ~ p ∧ q ≡ ~ p ∧ p ∧ q as   ~ ~ A ≡ A ≡ p ∧ q ∧ ~ p