Rule of Addition/Sequent Form/Formulation 1/Form 2
Jump to navigation
Jump to search
Theorem
| \(\ds q\) | \(\) | \(\ds \) | ||||||||||||
| \(\ds \vdash \ \ \) | \(\ds p \lor q\) | \(\) | \(\ds \) |
Proof 1
By the tableau method of natural deduction:
| Line | Pool | Formula | Rule | Depends upon | Notes | |
|---|---|---|---|---|---|---|
| 1 | 1 | $q$ | Premise | (None) | ||
| 2 | 1 | $p \lor q$ | Rule of Addition: $\lor \II_2$ | 1 |
$\blacksquare$
Proof by Truth Table
We apply the Method of Truth Tables.
$\begin{array}{|c||ccc|} \hline q & p & \lor & q \\ \hline \F & \F & \F & \F \\ \T & \F & \T & \T \\ \F & \T & \T & \F \\ \T & \T & \T & \T \\ \hline \end{array}$
As can be seen, when $q$ is true so is $p \lor q$.
$\blacksquare$