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Set union calculator

World's simplest set tool

With this online application, you can quickly find the union of two or more sets. The input sets can have different cardinalities and their format can be configured in the options. If you enable the option that allows repeated elements, then all sets are treated as multisets (sets that allow element copies) and in the output, you'll also get a multiset. Additionally, you can change the format of the output set and also sort the elements alphabetically or alphanumerically. Created by team Browserling.
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Format of Input Sets
The delimiter character that separates the input sets. (The default is three dashes.)
The delimiter character that separates input set elements.
Symbol that starts a set.
Symbol that ends a set.
Format of Set Union
If selected, the output set will be a multiset that allows duplicate elements.
The delimiter character that separates set union elements.
Symbol that starts a set.
Symbol that ends a set.
Set Union Sorting
Preserve the order of elements as they are in the input sets.
Rearrange the elements of the output set in alphabetical order.
Rearrange the elements of the output set in alphanumerical order.
Set union calculator tool What is a set union calculator?
This browser-based program applies the set union operation on multiple sets. The result of the union of two sets A and B is a set C, which is a collection of all elements of set A and all elements of set B. The set union operation is denoted by the symbol ∪ and it's a binary operation. In mathematical terms, the union of sets A and B is defined as follows: A∪B = {x: x ∈ A or x ∈ B}. For example, the union of two sets A = {1, 2, 3} and B = {4, 5} is the set {1, 2, 3, 4, 5}. The union of three sets A = {1, 2, 3}, B = {4, 5}, and C = {a, b} is the set {1, 2, 3, 4, 5, a, b}. To find the union of several sets, you need to enter all of them in the input field separated by the set separator character. By default, individual sets are separated by the string with three dashes "---", however, you can change the set string separator in the options. All entered sets must use the same style. It can be a classic set style with braces, for example, {a, b, c}, or a rarer set style, for example, [a; b; c]. The style of a set can be adjusted using the set element delimiter option and the side character option (for characters on the sides of a set). By default, the output union set is not a multiset, meaning that if sets A and B contain the same element, then in the output it's displayed only once. For example, for A = {1, 2, 3} and B = {2, 3, 4} the union is {1, 2, 3, 4}. If you enable the "Allow Repeated Elements" option, you will get a union multiset that contains element copies {1, 2, 3, 2, 3, 4}. Also, by default, given input sets A, B, C, D, …, the elements in the union will appear in the order they are in the input sets. An additional feature lets you sort the output set alphabetically or alphanumerically. Setabulous!
Set union calculator examples Click to use
Union of Two Sets
In this example, we find the union of two sets of integers. Both sets have cardinalities of 3 (meaning each has 3 elements in it) and they are written in Roster notation (also known as enumeration notation) that explicitly lists all members of each set. We separate both sets with three dashes and use the standard set formatting options with curly braces around set elements and commas between set elements. The output set, which is the union of both input sets has a cardinality of 5 because both input sets contain the same number "2". Mathematical sets contain only distinct objects and this is why the number "2" wasn't duplicated. However, there's also something called a multiset that permits repeating objects. If you activate the "Allow Repeated Elements" option, then the integer "2" will be duplicated two times.
{1, 2, 4} --- {2, 5, 8}
{1, 2, 4, 5, 8}
Required options
These options will be used automatically if you select this example.
The delimiter character that separates the input sets. (The default is three dashes.)
The delimiter character that separates input set elements.
Symbol that starts a set.
Symbol that ends a set.
If selected, the output set will be a multiset that allows duplicate elements.
The delimiter character that separates set union elements.
Symbol that starts a set.
Symbol that ends a set.
Preserve the order of elements as they are in the input sets.
2D and 3D Coordinate Points
In this example, the input sets are coordinate points in two-dimensional and three-dimensional spaces. The coordinates are semicolon-separated and the sets are enclosed in round parentheses. The delimiter character between the sets is the newline character "\n", which means that each set is on a new line. We enter all these characters in the input set style options but for the output set style, we use commas instead of semicolons. We also sort the set union alphanumerically that makes all numeric values go from the smallest to largest and all letters go alphabetically from a to z.
(0; 0) (-2; -3) (3; 4; 6) (z; x; y) (i; j; k)
(-3, -2, 0, 3, 4, 6, i, j, k, x, y, z)
Required options
These options will be used automatically if you select this example.
The delimiter character that separates the input sets. (The default is three dashes.)
The delimiter character that separates input set elements.
Symbol that starts a set.
Symbol that ends a set.
If selected, the output set will be a multiset that allows duplicate elements.
The delimiter character that separates set union elements.
Symbol that starts a set.
Symbol that ends a set.
Rearrange the elements of the output set in alphanumerical order.
Multiset Union
In this example, we load three multisets of different cardinalities and contents in the input box and separate them with the union symbol ∪. The first multiset consists of numbers, the second multiset consists of Latin letters, and the third multiset consists of ASCII symbols. They are all wrapped in square brackets and use a space to separate the elements. When calculating the union of these three multisets, we activate the option "Allow Repeated Elements". As a result, the output set is also made to be a multiset and all duplicate numbers, letters, and symbols in the input sets are copied to the output set. We also sorted the output set in alphabetical order and customized the output set format by entering angle brackets as the set wrapper symbols.
[0 5 5 20 100 -9] ∪ [s e t t o o l s] ∪ [! ^ _ ^ !]
<! ! -9 0 100 20 5 5 ^ ^ _ e l o o s s t t>
Required options
These options will be used automatically if you select this example.
The delimiter character that separates the input sets. (The default is three dashes.)
The delimiter character that separates input set elements.
Symbol that starts a set.
Symbol that ends a set.
If selected, the output set will be a multiset that allows duplicate elements.
The delimiter character that separates set union elements.
Symbol that starts a set.
Symbol that ends a set.
Rearrange the elements of the output set in alphabetical order.
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/find-set-union?input=%7B1%2C%202%2C%204%7D%0A---%0A%7B2%2C%205%2C%208%7D&input-set-separator=---&input-element-separator=%2C%20&input-open-set=%7B&input-close-set=%7D&allow-repetitions=false&output-element-separator=%2C%20&output-open-set=%7B&output-close-set=%7D&do-not-sort=true
All set tools
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Quickly find the powerset P(S) of the given set S.
Quickly reverse the order of elements in an ordered set.
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.
Coming soon These set tools are on the way
Draw a Venn Diagram
Illustrate two or more sets as a Venn diagram.
Find Set Symmetric Difference
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 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 Elements
Find all duplicate elements in a set.
Remove Duplicate Elements
Delete all duplicate elements from a set (leave unique).
Print Unique Elements
Find all unique elements in a set.
Remove Unique 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.