Symmetric difference

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

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 $A\triangle B=A\cup B$.