1. ## proof

Prove A U B= B U A

I know this seems really obvious but I can't figure out how to formally prove it.
Thanks!

2. The disjunctive or is commutative.

A or B is the same as B or A

$x \in A\; \vee \,x \in B$ is the same as $x \in B\; \vee \,x \in A$.

3. I need to write up a proof of why that is true though

4. The reason it is true is that or, $\vee$, is commutative.
That is the entire proof.
$\begin{gathered}
x \in \left( {A \cup B} \right)\; \Leftrightarrow x \in A \vee x \in B \hfill \\
x \in A \vee x \in B \equiv x \in B \vee x \in A \hfill \\
x \in B \vee x \in A \Leftrightarrow x \in \left( {B \cup A} \right) \hfill \\
\end{gathered}$