Term

symmetric difference, n.
(sets) The symmetric difference of sets A and B is the set of all elements of A or B which are not in both A and B.  Symbolically,
A Δ B = {x|(x ∈ A ∧ x ∉ B) ∨ (x ∉ A ∧ x ∈ B)}

Symbol

Δ
(sets) symmetric difference

Notation

symmetric difference
The symmetric difference of two sets A and B i s denoted by Δ, e.g.,
{a, b} Δ {b, c} = {a, c}

Venn Diagram

Venn Diagram for Set Symmetric Difference

Closure

symmetric difference
=`The set of sets is closed under symmetric difference.  That is, the symmetric difference of two sets is a set.

Associativity

symmetric difference
Difference of sets is associative: that is, for all sets A, B, and C,
(A Δ B) Δ C = A Δ (B Δ C)

Commutativity

symmetric difference
Symmetric difference of sets is commutative: that is, for all sets A and B,
A Δ B = B Δ A

Identities

symmetric difference
The empty set, ∅, is a right identity for set difference.  that is, for any set A,
A Δ &empty = A
The empty set, ∅, is a leftt identity for set difference.  that is, for any set A,
&empty Δ A = A

Idempotency

symmetric difference
Sets are not idempotent under symmetric difference: that is, in general, for set A,
A Δ A = ∅ ≠ A

Notation

symmetric difference
The symmetric difference of two sets A and B i s denoted by Δ, e.g.,
{a, b} Δ {b, c} = {a, c}

Remarks

Reference Links

Set Difference Math Now

External Links

Wikipedia Symmetric difference
Math World Symmetric Difference
NIST symmetric set difference