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

Theorem

 * $p \implies q \dashv \vdash \neg p \lor q$

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.

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