JEE Main201912 Jan 2019Morning ShiftMathematicsMathematical ReasoningActual
The Boolean expression p ∧ q ∨ p ∨ ~ q ∧ ~ p ∧ ~ q is equivalent to
Options
- Ap ∧ ~ q
- B~ p ∧ ~ q
- Cp ∨ ~ q
- Dp ∧ q
Correct answer
B. ~ p ∧ ~ q
Step-by-step solution
p ∧ q   ≡ b p ∨ ~ q   ≡ a + b + d ~ p ∧ ~ q   ≡ d ∴ p ∧ q ∨ p ∨ ~ q ≡ a + b + d p ∧ q ∨ p ∨ ~ q ∧ ~ p ∧ ~ q ≡ d ≡ ~ p ∧ ~ q