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!
The reason it is true is that or, $\displaystyle \vee $, is commutative.
That is the entire proof.
$\displaystyle \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} $