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 | 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. Buy the book
  2. power set. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 3/12/2009. http://www.merriam-webster.com/dictionary/power set.

More Information

  • 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.

Cite this article as:

McAdams, David E. Power Set. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/powerset.html.

Revision History

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.)
12/13/2008: Added example. (McAdams, David E.)
3/29/2008: Initial version. (McAdams, David E.)

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