Pronunciation: /ˈyun yən/ ?

A series of images showing that the union of A and B is everthing that is part of either A or B or both.
Figure 1: Click on the image to see a representation of C = A ∪ B.

A union of two or more sets is the set containing all the members of each of the sets. We say, "Set C is the union of sets A and B." We write C = A ∪ B.

Properties of Union of Sets

PropertyMath StatementDescription
CommutativeA ∪ B = B ∪ AThe union of sets is commutative
Associative(D ∪ E) ∪ F = D ∪ (E ∪ F)The union of sets is associative
Distributive(D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F)
(D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)
The intersection and union of sets are distributive


  1. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 5. Thomson, Brooks/Cole, 2005.
  3. Union. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=union&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

More Information

  • McAdams, David. Sets. LifeIsAStoryProblem.org. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.org/algebra/sets.html.
  • McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15. http://www.allmathwords.org/article.aspx?lang=en&id=Set.

Printed Resources

Cite this article as:

Union. 2008-09-15. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/u/union.html.


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Revision History

2008-09-15: Expanded 'More Information' (McAdams, David.)
2008-03-28: Added properties of union of sets (McAdams, David.)
2007-08-01: Initial version (McAdams, David.)

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