I find your notation confusing. Using a standard order of operation here is my take.
$\begin{gathered}
\left\{ {(p \vee \neg q) \wedge (\neg p \vee \neg q)} \right\} \vee q &\equiv \left\{ {(p \wedge \neg p) \vee \neg q} \right\} \vee q \\
&\equiv \left\{ {(F) \vee \neg q} \right\} \vee q \\
&\equiv \left\{ {\neg q} \right\} \vee q \\
&\equiv T \\
\end{gathered} $