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
 McAdams, David E.. All Math Words Dictionary, union. 2nd Classroom edition 201501084799968. pg 186. Life is a Story Problem LLC. January 8, 2015. Buy the book
 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
 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
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.)