Rule of Commutation/Disjunction/Formulation 1/Proof 2

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, in both cases, the truth values under the main connectives match for all boolean interpretations.

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