Power set

This page is the answer to the task Power set in the 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 {{}, {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 2ⁿ elements, including the edge cases of empty set. The power set of the empty set is the set which contains itself (2⁰ = 1): $\text{[math]}$ ( $\text{[math]}$ ) = { $\text{[math]}$ } 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 (2¹ = 2): $\text{[math]}$ ({ $\text{[math]}$ }) = { $\text{[math]}$ , { $\text{[math]}$ } } Extra credit: Demonstrate that your language supports these last two powersets.

No programs needed. Power set is intrinsically supported in Fōrmulæ.

Contents