Exclusive Or is Associative

Theorem
Exclusive or is associative:
 * $p \oplus \left({q \oplus r}\right) \dashv \vdash \left({p \oplus q}\right) \oplus r$

Proof
We apply the Method of Truth Tables.

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

$\begin{array}{|ccccc||ccccc|} \hline p & \oplus & (q & \oplus & r) & (p & \oplus & q) & \oplus & r \\ \hline F & F & F & F & F & F & F & F & F & F \\ F & T & F & T & T & F & F & F & T & T \\ F & T & T & T & F & F & T & T & T & F \\ F & F & T & F & T & F & T & T & F & T \\ T & T & F & F & F & T & T & F & T & F \\ T & F & F & T & T & T & T & F & F & T \\ T & F & T & T & F & T & F & T & F & F \\ T & T & T & F & T & T & F & T & T & T \\ \hline \end{array}$