Official solution
We know, p \[ \leftrightarrow \] q \[ \equiv \] \[\left( {p \to q} \right) \wedge \left( {q \to p} \right)\]
\[ \therefore \] x \[ \leftrightarrow \] ~ y \[ \equiv \] \[\left( {x \to \sim y} \right) \wedge \left( { \sim y \to x} \right)\]
[ Also \[p \to q \equiv \sim p \vee q\] ]
\[ \Rightarrow \] x \[ \leftrightarrow \] ~ y \[ \equiv \] \[\left( { \sim x \vee \sim y} \right) \wedge \left( {y \vee x} \right)\]
\[ \therefore \] \[ \sim \left( {x \leftrightarrow \sim y} \right) \equiv \left( {x \wedge y} \right) \vee \left( { \sim y \wedge \sim x} \right)\]