Symmetric difference

A symmetric difference of sets $A$ and $B$ is the set of elements that belong to exactly one of them:

A\triangle B=(A\setminus B)\cup(B\setminus A).

Remarks

This operation is built from set difference and union. It is symmetric in $A$ and $B$ and measures “disagreement” between sets: $A\triangle B=\varnothing$ exactly when $A=B$ .

Examples

$\{1,2,3\}\triangle\{2,3,4\}=\{1,4\}$ .
If $A$ and $B$ are disjoint, then $A\triangle B=A\cup B$ .