In
mathematics, the
symmetric difference of two
sets is the set of elements which are in either of the sets and not in their intersection. The symmetric difference of the sets
A and
B is commonly denoted by
or
or
For example, the symmetric difference of the sets
and
is
. The symmetric difference of the set of all students and the set of all females consists of all male students together with all female non-students.
The
power set of any set becomes an
abelian group under the operation of symmetric difference, with the
empty set as the
neutral element of the group and every element in this group being its own
inverse. The power set of any set becomes a
Boolean ring with symmetric difference as the addition of the ring and
intersection as the multiplication of the ring.
Venn diagram of
The symmetric difference is
the
unionwithout the
intersection:
×