Power set
This page is the answer to the task Power set in the Rosetta Code.
Description (from Rosetta Code)
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 power set (or powerset) of S, written P(S), or 2^{S}, 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^{S} of S. For example, the power set of {1,2,3,4} is
For a set which contains n elements, the corresponding power set has 2^{n} elements, including the edge cases of empty set. The power set of the empty set is the set which contains itself (2^{0} = 1):
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^{1} = 2):
Extra credit: Demonstrate that your language supports these last two powersets. |
Program
No programs needed. Power set is intrinsically supported in Fōrmulæ.