Rule of Material Implication/Formulation 1

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Theorem

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


This can be expressed as two separate theorems:

Forward Implication

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

Reverse Implication

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


Proof by Truth Table

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.

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

$\blacksquare$


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