# Rule of Conjunction/Sequent Form/Formulation 1/Proof 2

## Theorem

$p, q \vdash p \land q$

## Proof

We apply the Method of Truth Tables.

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

As can be seen, only when both $p$ and $q$ are true, then so is $p \land q$.

$\blacksquare$