JEE Main202315 Apr 2023Morning ShiftMathematicsMathematical ReasoningActual
Negation of p ∧ q ∧ ~ p ∧ q is
Options
- A~ p ∧ q ∨ p
- Bp ∨ q
- C~ p ∨ q
- D~ p ∧ q ∧ q
Correct answer
A. ~ p ∧ q ∨ p
Step-by-step solution
Given, Expression p ∧ q ∧ ~ p ∧ q So, negation of the above expression will be, ~ p ∧ q ∧ ~ p ∧ q Now using demorgan's law ~ A ∧ B ≡ ~ A ∨ ~ B   &   ~ A ∨ B ≡ ~ A ∧ ~ B we get, ~ p ∧ q ∧ ~ p ∧ q ≡ ~ p ∧ q ∧ ~ p ∨ ~ q ≡ ~ p ∧ q ∧ ~ p ∨ q ∧ ~ q ≡ ~ p ∧ q ∧ ~ p ∨ F ≡ ~ p ∧ q ∧ ~ p ≡ ~ p ∨ ~ q ∧ ~ p &