Power Set

Pronunciation: /ˈpaʊ ər sɛt/ ?

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


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


  1. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 5. Thomson, Brooks/Cole, 2005.
  2. power set. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/power set.

More Information

  • McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15. http://www.allmathwords.org/article.aspx?lang=en&id=Set.

Printed Resources

Cite this article as:

Power Set. 2009-12-15. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/powerset.html.


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Revision History

2009-12-15: Corrected equations: changed symbol for subset to symbol for subset or equal to. (McAdams, David.)
2008-12-13: Added example (McAdams, David.)
2008-03-29: Initial version (McAdams, David.)

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