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# 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.

## Additional terminology

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
elements.

Two sets are *disjoint* if they have no elements in common, that is,
if A
B = .

Copyright © 1996 by David Matuszek

Last modified Feb 2, 1996