Let $p$ and $q$ be two statements, then $q\leftrightarrow (~p\vee ~q)$is logically equivalent to

$$\begin{gathered} q\leftrightarrow (~p\vee ~q) \\ \begin{array}{l}\equiv q\leftrightarrow \sim (p\wedge q)\\ \equiv [q\to \sim (p\wedge q\left)\right]\wedge [~(p\wedge q)\to q]\\ \equiv [~q\vee ~(p\wedge q\left)\right]\wedge \left[\right(p\wedge q)\vee q]\\ \equiv \sim [q\wedge (p\wedge q\left)\right]\wedge q\\ \equiv \sim (p\wedge q)\wedge q\\ \equiv (~p\vee ~q)\wedge q\\ \equiv (~p\wedge q)\vee (~q\wedge q)\\ \equiv (~p\wedge q)\end{array} \end{gathered}$$