Rule of Commutation/Conjunction/Formulation 1/Proof by Truth Table

Theorem

 * $p \land q \dashv \vdash q \land p$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all [[Definition:Boolean Interpretation|boolean interpretations].

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