Official solution
((p \[ \wedge \] q) \[ \vee \] (p \[ \vee \] \[ \sim \] q)) \[ \wedge \] (\[ \sim \] p \[ \wedge \] \[ \sim \] q)
\[ \equiv \] \[\left( {\left( {\left( {p \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( {q \vee \left( {p \vee \sim q} \right)} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {\left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {\left( {p \vee \sim q} \right) \wedge \left( {t \vee p} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {\left( {p \vee \sim q} \right) \wedge t} \right) \wedge \left( { \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {p \vee \sim q} \right) \wedge \left( { \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {p \wedge \sim p \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p \wedge \sim q} \right)\]
\[ \equiv \] \[\left( {f \wedge \sim q} \right) \vee \left( { \sim q \wedge \sim p} \right)\]
\[ \equiv \] \[f' \vee \left( { \sim q \wedge \sim p} \right)\]
\[ \equiv \] \[\left( { \sim q \wedge \sim p} \right)\]