# Powerset Generator

World's simplest set tool
With this online application, you can quickly find the power set P(S) of the given input set S. As the power set for an n element set is made out of 2

^{n}subsets, the input set size is limited to 16 elements, which will generate 65,536 subsets. In the options, you can control the generation order of subsets and also the order of elements within subsets. You can also customize the looks of the output power set and individual subsets. Created by team Browserling.
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## What is a Powerset Generator?

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This browser-based program generates all subsets of the given set. This is called the powerset and it includes the empty set and also the set itself. Given the set A, the usual notation for the powerset is P(A) or if you love fancy things, also 𝒫(A) and ℙ(A). If the cardinality (number of elements) of the input set A is n, then the powerset is made out of 2

^{n}elements. The number 2^{n}grows exponentially fast and for just 10 element set it already exceeds 1000. By default, the powerset generator prints subsets from the one with least elements to the one with most elements – first, it's the empty set, then the singleton subsets, then the two-element subsets, and so on. You can also change the order of this output in the options and display subsets from the one with most elements to the one with least elements or print them in random order. You can also change the order of elements in the subsets – they can go from left to right, from right to left, or in random order. As different programming languages use different syntax for sets, you can also customize the format of the output subsets – you can change the open-set symbol "{" and the close-set symbol "}" and change the set element delimiter "," to something else. Setabulous!## Powerset Generator examples

Click to usePowerset of 4 Elements

In this example, we generate a powerset from a four-element set. The elements of this set are digits from 1 to 4 and the set is entered using standard mathematical notation, where commas separate the elements and the set is enclosed in curly brackets. The powerset of a set of four elements creates 2

^{4}= 16 subsets. We generate them in order of their cardinality (from the smallest subset to the largest subset) and also use the standard set format in the output.
{1, 2, 3, 4}

{}
{1}
{2}
{3}
{4}
{1, 2}
{1, 3}
{1, 4}
{2, 3}
{2, 4}
{3, 4}
{1, 2, 3}
{1, 2, 4}
{1, 3, 4}
{2, 3, 4}
{1, 2, 3, 4}

**Required options**

Enter the symbol that separates
the input set elements.

Open set symbol.

Close set symbol.

Enter the symbol that separates
the elements of individual subsets.

Enter the symbol that separates
the generated subsets.

Open set symbol.

Close set symbol.

Power Set of the Alphabet

This example loads a set of first five English letters as input elements and returns the power set of 32 sets in the output. It changes the subset order in the output and first prints the 5-element set with all the letters (same as input set), then all possible 4-element sets with all possible four-letter combinations, then all possible 3-element sets with three letters, then 2-element sets with two letters, then 1-element sets, and then the only 0-element set (null set). It also changes the letter order and takes the elements from the input set from right to left when creating subsets. It uses angle brackets as set-open and set-close characters, removes separators between set elements, and prints all subsets on one line, separated by commas.

{a, b, c, d, e}

<edcba>, <dcba>, <ecba>, <edba>, <edca>, <edcb>, <cba>, <dba>, <dca>, <dcb>, <eba>, <eca>, <ecb>, <eda>, <edb>, <edc>, <ba>, <ca>, <cb>, <da>, <db>, <dc>, <ea>, <eb>, <ec>, <ed>, <a>, <b>, <c>, <d>, <e>, <>

**Required options**

Enter the symbol that separates
the input set elements.

Open set symbol.

Close set symbol.

Enter the symbol that separates
the elements of individual subsets.

Enter the symbol that separates
the generated subsets.

Open set symbol.

Close set symbol.

Unicode Powerset

In this example, we enter a very unusual set in the input and get an even more unusual powerset in the output. Each element of the input set is a Unicode fruit emoji. As the input emojis are separated by spaces and there are no open/close set symbols around the set elements, in the options we use the space character as the input element separator and leave the open/close set character fields empty. Additionally, we use the bold curly brackets to enclose the fruit subsets and put the "❌" symbol between subset elements.

🍍 🍎 🥝 🍇

❴❵
❴🍍❵
❴🍎❵
❴🥝❵
❴🍇❵
❴🍍❌🍎❵
❴🍍❌🥝❵
❴🍍❌🍇❵
❴🍎❌🥝❵
❴🍎❌🍇❵
❴🥝❌🍇❵
❴🍍❌🍎❌🥝❵
❴🍍❌🍎❌🍇❵
❴🍍❌🥝❌🍇❵
❴🍎❌🥝❌🍇❵
❴🍍❌🍎❌🥝❌🍇❵

**Required options**

Enter the symbol that separates
the input set elements.

Open set symbol.

Close set symbol.

Enter the symbol that separates
the elements of individual subsets.

Enter the symbol that separates
the generated subsets.

Open set symbol.

Close set symbol.

Pro tips
Master online set tools

You can pass input to this tool via

__?input__query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinesettools.com/generate-powerset

__?input__=%7B1%2C%202%2C%203%2C%204%7D&input-element-separator=%2C%20&input-open-set=%7B&input-close-set=%7D&output-element-separator=%2C%20&output-subset-separator=%5Cn&output-open-set=%7B&output-close-set=%7D&subset-order=least-to-most&element-order=left-to-right
All set tools

Quickly find the powerset P(S) of the given set S.

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Quickly find the number of elements in a set.

Quickly apply the set union operation on two or more sets.

Quickly apply the set intersection operation on two or more sets.

Quickly apply the set difference operation on two or more sets.

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Illustrate two or more sets as a Venn diagram.

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Apply the set difference operation on sets A and B.

Find Set Cartesian Product

Apply the set cartesian product operation on sets A and B.

Find All Subsets of a Set

Quickly find all sets that are subsets of set A.

Find All Set Permutations

Generate all permutations of set elements.

Enumerate a Set

Add numbering to all set elements.

Filter a Set

Print set elements that match a filter.

Find Set Elements

Find elements in a set that match certain criteria.

Apply a Function on a Set

Run a function on all elements in a set.

Convert a Multiset to a Set

Convert a set with repeated elements to a standard set.

Convert a Set to a Multiset

Convert a standard set to a multiset with repeated elements.

Convert a Set to a List

Create a list from the given set.

Convert a List to a Set

Create a set from the given list.

Convert a Set to an Array

Create an array from the given set.

Convert an Array to a Set

Create a set from the given array.

Duplicate Set Elements

Repeat set elements multiple times.

Print Duplicate Set Elements

Find all duplicate elements in a set.

Remove Duplicate Set Elements

Delete all duplicate elements from a set (leave unique).

Print Unique Set Elements

Find all unique elements in a set.

Remove Unique Set Elements

Delete all unique elements from a set (leave duplicates).

Remove Empty Set Elements

Delete empty elements (zero-length elements) from a set.

Find Set Depth

Calculate how many levels of subsets a set has.

Flatten a Set

Decrease subset nesting.

Truncate a Set

Remove elements from a set and make it smaller.

Truncate Set Elements

Shorten all set elements to the given length.

Expand a Set

Add elements to a set and make it bigger.

Split a Set

Split a set into a certain number of subsets.

Join Sets

Merge multiple sets together to form one large set.

Slice a Set

Extract an index-based subset from a set.

Partition a Set

Find disjoint subsets of the given set whose union is the same set.

Randomize a Set

Randomly change the order of elements in a set.

Select a Random Set Element

Pick a random element from the given set.

Select a Random Subset

Pick a random subset of the given set.

Generate an Empty Set

Create a set with no elements.

Generate a Digit Set

Create a set that contains digits.

Generate a Number Set

Create a set that contains numbers.

Generate an Integer Set

Create a set that contains integers.

Generate a Decimal Set

Create a set that contains decimal fractions.

Generate a Letter Set

Create a set that contains letters.

Generate a Character Set

Create a set that contains characters.

Generate a Word Set

Create a set that contains words.

Generate a String Set

Create a set that contains strings.

Generate a Text Set

Create a set that contains text.

Generate a Sentence Set

Create a set that contains sentences.

Generate a Random Set

Create a set that contains random elements.

Generate a Custom Set

Create a custom set with custom elements and custom size.

Generate an Infinite Set

Create a set with infinitely many elements.

Generate a Finite Set

Create a set with a finite number of elements.

Change Set Notation

Change the open-set, close-set, and element separator symbols.

Change Set Size

Add or remove set elements to make it a certain size/length.

Destroy a Set

Launch a Zalgo attack on a set and destroy it.

Compare Sets

Find all differences between two or more sets.

Symmetrize a Set

Convert a regular set to a symmetric multi-set.

Color a Set

Add colors to set elements.

Visualize a Set

Create an abstract visualization of a set.

Convert a Set to an Image

Create a downloadable picture from a set.

Print Set Analytics

Analyze a set and print its statistics.

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