How to negate if and only if How can I get $(A ↔ ¬B)$ or $(¬A ↔ B)$ from $¬(A ↔ B)$ using propositional laws?
I tried expanding $¬(A ↔ B)$ and I got to $(A ∧ ¬B) ∨ (B ∧ ¬A)$
I also tried expanding $(A ↔ ¬B)$ and I got to $(¬A ∨ ¬B) ∧ (B ∨ A)$
I don't know where in my expansion I went off the wrong path

Distribute:
$$(A\land\lnot B)\lor(B\land\lnot A)=(A\lor B)\land(\lnot B\lor B)\land(A\lor\lnot A)\land(\lnot B\lor\lnot A)$$
and then recognize that $(P\lor\lnot P)$ is always true, so the middle two pairs drop out and the right hand side reduces to
$$(A\lor B)\land(\lnot B\lor\lnot A)$$
