Power set: Difference between revisions

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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 2S, is the set of all subsets of S.

Given a set S, the [[wp:Power_set|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 [[wp:Empty_set|empty set]].

The power set of the empty set is the set which contains itself (20 = 1):

<math>\mathcal{P}</math>(<math>\varnothing</math>) = { <math>\varnothing</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):

<math>\mathcal{P}</math>({<math>\varnothing</math>}) = { <math>\varnothing</math>, { <math>\varnothing</math> } }

=={{header|Ada}}==

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 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.<br>
+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.<br />
 '''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 {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 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> } }
 =={{header|Ada}}==