The set of elements belonging to one but not both of two given sets. It is therefore the union of the complement of with respect to and with respect to , and corresponds to the XOR operation in Boolean logic. The symmetric difference can be implemented in the Wolfram Language as:
SymmetricDifference[a_, b_] := Union[Complement[a, b], Complement[b, a]]
The symmetric difference of sets and is variously written as , , (Borowski and Borwein 1991) or (Harris and Stocker 1998, p. 3). All but the first notation should probably be deprecated since each of the other symbols has a common meaning in other areas of mathematics.
For example, for and , , since 2, 3, and 5 are each in one, but not both, sets.