RosettaCodeData/Task/Power-set/00DESCRIPTION

{{omit from|GUISS}}

A   [[set]]   is a collection (container) of certain values,
without any particular order, and no repeated values.

It corresponds with a finite set in mathematics.

A set can be implemented as an associative array (partial mapping)
in which the value of each key-value pair is ignored.

Given a set S, the [[wp:Power_set|power set]] (or powerset) of S, written P(S), or 2<sup>S</sup>, is the set of all subsets of S.


;Task:
By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2<sup>S</sup> of S.


For example, the power set of &nbsp; &nbsp; {1,2,3,4} &nbsp; &nbsp; is
::: {{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.

For a set which contains n elements, the corresponding power set has 2<sup>n</sup> elements, including the edge cases of [[wp:Empty_set|empty set]].<br />

The power set of the empty set is the set which contains itself (2<sup>0</sup> = 1):<br />
::: <math>\mathcal{P}</math>(<math>\varnothing</math>) = { <math>\varnothing</math> }<br />

And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (2<sup>1</sup> = 2):<br />
::: <math>\mathcal{P}</math>({<math>\varnothing</math>}) = { <math>\varnothing</math>,  { <math>\varnothing</math> } }<br>


'''Extra credit: ''' Demonstrate that your language supports these last two powersets.
<br><br>