Rule of Material Implication/Formulation 1/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.

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