# Rule of Addition/Sequent Form/Formulation 1/Form 1

## Theorem

$p \vdash p \lor q$

## Proof 1

By the tableau method of natural deduction:

$p \vdash p \lor q$
Line Pool Formula Rule Depends upon Notes
1 1 $p$ Premise (None)
2 1 $p \lor q$ Rule of Addition: $\lor \mathcal I_1$ 1

$\blacksquare$

## Proof 2

We apply the Method of Truth Tables.

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

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

$\blacksquare$