Correct Answer - Option 1 : P ↔ ¬ Q
Formula:
¬ (P ↔ Q) = (¬P ↔ Q) = (P ↔ ¬Q)
Truth Table:
|
P
|
¬ P
|
Q
|
¬ Q
|
¬ (P ↔ Q)
|
¬ P ↔ Q
|
P ↔ ¬ Q
|
¬ P ↔ ¬ Q
|
Q → P
|
|
F
|
T
|
F
|
T
|
F
|
F
|
F
|
T
|
T
|
|
F
|
T
|
T
|
F
|
T
|
T
|
T
|
F
|
F
|
|
T
|
F
|
F
|
T
|
T
|
T
|
T
|
F
|
T
|
|
T
|
F
|
T
|
F
|
F
|
F
|
F
|
T
|
T
|
Therefore, ¬ (P ↔ Q) is equivalent to (¬P ↔ Q) and (P ↔ ¬Q)
Hence option 1 is correct.
Important Points:
(P ↔ Q) ≡ p ⊙ q
¬ (P ↔ Q) ≡ p ⊕ q
Option 2: ¬ P ↔ Q is changed to ¬ P → Q
