Terms

set difference, n.
(sets) The difference of sets A and B is the set of all elements of A which are not also elements of B.  Symbolically,
A - B = {x|x ∈ A ∧ x ¬in B}
relative complement, n.
(math) See set difference.

Symbols

-
(sets) set difference
\
(sets) set difference

Venn Diagram

Venn Diagram for Set Difference

Closure

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

Associativity

set difference
Difference of sets is not associative: that is, in general, for sets A, B, and C,
(A - B) - C ≠ A - (B - C)

Commutativity

set difference
Difference of sets is not Commutative: that is, in general for sets A and B,
A - B ≠ B - A

Identities

set difference
The empty set, ∅, is a right identity for set difference.  that is, in general, for set A,
A - &empty = A
There is no left identity for set difference.

Idempotency

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

Terms

set difference, n.
(sets) The difference of sets A and B is the set of all elements of A which are not also elements of B.  Symbolically,
A - B = {x|x ∈ A ∧ x ¬in B}
relative complement, n.
(math) See set difference.

Notation

Remarks

Reference Links

Set Symmetric Difference Math Now

External Links

Wikipedia Complement (Set Theory)
Math World Set Difference
NIST difference