An operation on sets. Let $A$ and $B$ be two sets (where the second need not be contained in the first). Then the set of those elements of $A$ that are not elements of $B$ is called the difference of these sets.

The difference between two sets $A$ and $B$ is denoted by $A\setminus B$.


Comments

When $B$ is a subset of $A$, the difference is often termed the complement or relative complement of $B$ in $A$.

See also Symmetric difference of sets.

References

[a1] P. R. Halmos, Naive Set Theory, Springer (1960) ISBN 0-387-90092-6
How to Cite This Entry:
Difference of two sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Difference_of_two_sets&oldid=53846
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article