Rule of Addition/Sequent Form/Formulation 1/Form 2/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

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

As can be seen, when $q$ is true so is $p \lor q$.