Pronunciation: /ˈyun yən/ Explain

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. Last Accessed 1/24/2010. Buy the book
  2. 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. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/u/union.html.

Image Credits

Revision History

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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