Rule of Commutation/Disjunction/Formulation 2/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connective match for all boolean interpretations.

$\begin{array}{|ccc|c|ccc|} \hline (p & \lor & q) & \iff & (q & \lor & p) \\ \hline \F & \F & \F & \T & \F & \F & \F \\ \F & \T & \T & \T & \T & \T & \F \\ \T & \T & \F & \T & \F & \T & \T \\ \T & \T & \T & \T & \T & \T & \T \\ \hline \end{array}$