View source for Symmetric difference

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==Definition==
Let {{M|A,B\in\mathcal{P}(X)}} be two [[subset|subsets]] of a [[set]] {{M|X}}. We define the ''symmetric difference'' of {{M|A}} and {{M|B}} as{{rMTH}}:
* {{M|1=A\triangle B:=(A-B)\cup(B-A)}}<ref group="Note">Here {{M|A-B}} denotes ''[[set subtraction]]''.</ref>
** In words: {{M|A\triangle B}} contains (everything in {{M|A}} and not in {{M|B}}) and (everything in {{M|B}} but not in {{M|A}}).
'''Claim 1: ''' this is equivalent to {{M|1=A\triangle B:=(A\cap B^C)\cup(A^C\cap B)}}<ref name="MTH"/>
==Proof of claims==
{{Requires proof|Trivial, be bothered to show this}}
==Notes==
<references group="Note"/>
==References==
<references/>
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{{Definition|Set Theory|Measure Theory}}
[[Category:Set operations]]