# Power Set

Pronunciation: /ˈpaʊ.ər sɛt/ Explain

Given a set A, the power set of A is all the subsets of A. This is written in set notation as ℘( A ) = { X | XA }. Note that the empty set is always a member of every power set and every set is a member of its own power set.

### Example

Given set B = {3, 7, 8}, the power set of B is defined as ℘( B ) = { X | XB } = { {}, {3}, {7}, {8}, {3, 7}, {3, 8}, {7, 8}, {3, 7, 8} }.

### References

1. McAdams, David E.. All Math Words Dictionary, power set. 2nd Classroom edition 20150108-4799968. pg 143. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 5. Thomson, Brooks/Cole. 2005. Buy the book

• McAdams, David E.. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 12/15/2009. http://www.allmathwords.org/en/s/set.html.

McAdams, David E. Power Set. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/powerset.html.

### Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/15/2009: Corrected equations: changed symbol for subset to symbol for subset or equal to. (McAdams, David E.)