Rule of Commutation/Disjunction/Formulation 1/Proof 2

Theorem

 * $p \lor q \dashv \vdash q \lor p$

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.

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