JEE Main202226 Jul 2022Evening ShiftMathematicsMathematical ReasoningActual
Negation of the Boolean expression p ↔ q → p is
Options
- A~ p ∧ q
- Bp ∧ ~ q
- C~ p ∨ ~ q
- D~ p ∧ ~ q
Correct answer
D. ~ p ∧ ~ q
Step-by-step solution
To find ~ p ↔ q → p We know ~ p ↔ q ≡ p ∧ ~ q ∨ q ∧ ~ p So ~ p ↔ q → p ≡ p ∧ ~ q → p ∨ q → p ∧ ~ p Now p ∧ ~ q → p ≡ p ∧ q ∧ ~ p ≡ p ∧ ~ p ∧ q ≡ c and q → p ∧ ~ p ≡ ~ q ∨ p ∧ ~ p ≡ ~ p ∧ ~ q ∨ p ≡ ~ p ∧ ~ q ∨ ~ p ∧ p = ~ p ∧ ~ q Hence ~ p ↔ q → p ≡ c ∨ ~ p ∧ ~ q Ͱ