Power Set

The set of all subsets of a given set. For a set $A$ with $n$ elements, the power set $\mathcal{P}(A)$ contains $2^n$ subsets (including the Empty Set and $A$ itself).

Context

Power sets illustrate how quickly combinations grow. For example, if $A=\{1,2\}$, then $\mathcal{P}(A)=\{\varnothing ,\{1\},\{2\},\{1,2\}\}$ with $|\mathcal{P}(A)|=4$. Power sets are used in formal logic, topology, and database theory.

See Also

• set
• subset
• proper subset
• cardinality
• Empty Set