Union
Pronunciation: /ˈyun yən/ ?
 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
 Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 5. Thomson, Brooks/Cole, 2005.
 Union. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 20110108). 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. 20090312. http://www.lifeisastoryproblem.org/algebra/sets.html.
 McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20091215. http://www.allmathwords.org/article.aspx?lang=en&id=Set.
Printed Resources
Cite this article as:
Union. 20080915. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/u/union.html.
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20080915: Expanded 'More Information' (
McAdams, David.)
20080328: Added properties of union of sets (
McAdams, David.)
20070801: Initial version (
McAdams, David.)