The statement ~ p ⇔ q is not equivalent to

Step-by-step solution

Option A is theorem hence A is equivalent to ~ p ⇔ q Option B   ~ p ⇔ q means only p or only q Which is same as p ∧ ~ q ∨ q ∧ ~ p Option C   p ∨ q ∧ ~ p v ~ q ≡ p ∨ q ∧ ~ p ∧ q Means p ∨ q happens but p ∧ q does not happen. It means only p or only q happens Option D   ~ p ⇔ q ≡ p ∨ q ∨ ~ p ∧ q ≡ ~ p ∨ q ⇒ p ∧ q but not equivalent to p ∨ q ⇒ p ∧ q