Operations on Sets
- The union of sets A and B, written A
B, is a set that contains everything that is in A, or in B, or in both.
- The intersection of sets A and B, written A
B, is a set that contains exactly those elements that are in both A and B.
- The set difference of set A and set B, written A - B,
is a set that contains everything that is in A but not in B.
- The complement of a set A, written as -A or (better) A with
a bar drawn over it, is the set containing everything
that is not in A.
This is almost always used in the context of some universal set
U that contains "everything" (meaning "everything we are interested in
at the moment").
Then -A is shorthand for U - A.
The cardinality of a set A, written |A|, is
the number of elements in a set A.
The powerset of a set Q, written 2,
is the set of all subsets of Q. The notation suggests the fact that a set containing
n elements has a powerset containing 2
Two sets are disjoint if they have no elements in common, that is,
B = .
Copyright © 1996 by David Matuszek
Last modified Feb 2, 1996