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

Proof
We apply the Method of Truth Tables.

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

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