Pronunciation: /ˈjun.jən/ Explain

A series of images showing that the union of A and B is everything 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 = AB.

Properties of Union of Sets

PropertyMath StatementDescription
Commutative AB = BA The union of sets is commutative
Associative (DE) ∪ F = D ∪ (EF) The union of sets is associative
Distributive(DE) ∪ F = (DF) ∩ (EF)
(DE) ∩ F = (DF) ∪ (EF)
The intersection and union of sets are distributive


  1. McAdams, David E.. All Math Words Dictionary, union. 2nd Classroom edition 20150108-4799968. pg 186. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 12/17/2018. Buy the book
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 5. Thomson, Brooks/Cole. 2005. Buy the book

More Information

  • McAdams, David E.. Sets. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/algebra/sets.html.

Cite this article as:

McAdams, David E. Union. 5/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/u/union.html.

Image Credits

Revision History

5/13/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/16/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
9/15/2008: Expanded 'More Information'. (McAdams, David E.)
3/28/2008: Added properties of union of sets. (McAdams, David E.)
8/1/2007: Initial version. (McAdams, David E.)

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