Union

Pronunciation: /ˈjun.jən/ Explain

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 Property Math Statement Description Commutative A ∪ B = B ∪ A The 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

References

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. http://www.allmathwords.org/en/u/union.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.)