Exclusive Or is Commutative/Proof 2

Theorem
Exclusive or is commutative:


 * $p \oplus q \dashv \vdash q \oplus p$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all models.

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