Definition:Symmetric Difference

Definition
The symmetric difference between two sets $S$ and $T$ is written $S * T$ and is defined as:

Definition 5
where:
 * $\setminus$ denotes set difference
 * $\cup$ denotes set union
 * $\cap$ denotes set intersection
 * $\overline S$ denotes the complement of $S$
 * $\oplus$ denotes the exclusive or connective.

That is, it is the set of all elements of one of the two sets which are not also elements of the other set.

Also known as

 * Disjoint union
 * Boolean sum

Also see

 * Equivalence of Definitions of Symmetric Difference