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

Theorem

 * $q \vdash p \lor q$

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 $p \lor q$.