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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