\section{Symmetric Difference is Commutative}
Tags: Symmetric Difference, Commutativity

\begin{theorem}
[[Definition:Symmetric Difference|Symmetric difference]] is [[Definition:Commutative Operation|commutative]]:
:$S * T = T * S$
\end{theorem}

\begin{proof}
{{begin-eqn}}
{{eqn | l = S * T
      | r = \paren {S \setminus T} \cup \paren {T \setminus S}
      | c = {{Defof|Symmetric Difference}}
}}
{{eqn | r = \paren {T \setminus S} \cup \paren {S \setminus T}
      | c = [[Union is Commutative]]
}}
{{eqn | r = T * S
      | c = {{Defof|Symmetric Difference}}
}}
{{end-eqn}}
{{Qed}}
\end{proof}


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