Symmetric difference

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Find a ven diagram and make an infobox

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Definition

Let $A,B\in\mathcal{P}(X)$ be two subsets of a set $X$. We define the symmetric difference of $A$ and $B$ as:

• $A\triangle B:=(A-B)\cup(B-A)$
  • In words: $A\triangle B$ contains (everything in $A$ and not in $B$) and (everything in $B$ but not in $A$).

Claim 1: this is equivalent to $A\triangle B:=(A\cap B^C)\cup(A^C\cap B)$

Proof of claims

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Trivial, be bothered to show this