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 2S, 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 2S 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):


 





P




{\displaystyle {\mathcal {P}}}

(



∅


{\displaystyle \varnothing }

) = { 



∅


{\displaystyle \varnothing }

 }

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):


 





P




{\displaystyle {\mathcal {P}}}

({



∅


{\displaystyle \varnothing }

}) = { 



∅


{\displaystyle \varnothing }

, { 



∅


{\displaystyle \varnothing }

 } }


Extra credit:  Demonstrate that your language supports these last two powersets.




 
function power-set ($array) {
    if($array) {
        $n = $array.Count
        function state($set, $i){  
            if($i -gt -1) {
                state $set ($i-1)
                state ($set+@($array[$i])) ($i-1)   
            } else {
                "$($set | sort)"
            }
        }
        $set = state @() ($n-1)
        $power = 0..($set.Count-1) | foreach{@(0)}
        $i = 0
        $set | sort | foreach{$power[$i++] = $_.Split()}
        $power | sort {$_.Count}
    } else {@()}
 
}
$OFS = " "
$setA = power-set  @(1,2,3,4)
"number of sets in setA: $($setA.Count)"
"sets in setA:"
$OFS = ", "
$setA | foreach{"{"+"$_"+"}"} 
$setB = @()
"number of sets in setB: $($setB.Count)"
"sets in setB:"
$setB | foreach{"{"+"$_"+"}"} 
$setC = @(@(), @(@()))
"number of sets in setC: $($setC.Count)"
"sets in setC:"
$setC | foreach{"{"+"$_"+"}"} 
$OFS = " "
 