Intersection of Sets
Pronunciation: /ˌɪn.tərˈsɛk.ʃən ʌv sɛtz/ Explain

Figure 1:
Intersection. Click on the image to see a representation of
A ∩ B. 

An intersection of two or more
sets
is a set containing the members that are in all of the sets. This is spoken, "Set
C is the intersection of sets
A and B."
This is written, C = A ∩ B.
Properties of Intersection of Sets
Property  Math Statement  Description 
Commutative 
A ∩ B = B ∩ A 
The intersection of sets is commutative 
Associative 
(D ∩ E) ∩ F = D
∩ (E ∩ F) 
The intersection 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 
Table 1: Properties of the intersection of two sets. 

References
 McAdams, David E.. All Math Words Dictionary, intersection. 2nd Classroom edition 201501084799968. pg 101. Life is a Story Problem LLC. January 8, 2015. Buy the book
 intersection. merriamwebster.com. Encyclopedia Britannica. MerriamWebster. Last Accessed 8/7/2018. http://www.merriamwebster.com/dictionary/intersection. Buy the book
 Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior. 3rd edition. pg 63. www.archive.org. Princeton University Press. 1953. Last Accessed 8/7/2018. http://www.archive.org/stream/theoryofgamesand030098mbp#page/n84/mode/1up. Buy the book
 Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 8/7/2018. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 4. Thomson, Brooks/Cole. 2005. Last Accessed 8/7/2018. 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. Intersection of Sets. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/i/intersection.html.
Image Credits
Revision History
4/23/2019: Updated equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
7/30/2018: Initial version. (
McAdams, David E.)