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

Theorem

 * $\left({p \lor q}\right) \iff \left({q \lor p}\right)$

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.

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