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Set Calculator

Last updated date: 16th May 2024
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Set Finder

In mathematics, Set calculator deals with a finite assemblage of objects, be it numbers, letters, or any real-world objects. Sometimes a necessity takes place wherein we require setting up a relationship between two sets. There comes the concept of set operations and the need of a set finder.

In this chapter, you will have an understanding of the various notations of representing sets, how to operate on sets and their application in real life.

Use of a Set Calculator

You can use the set operations calculator in order to:

  • Identify the union of sets

  • Intersection of sets

  • Differences between sets!

All you need to do is just enter the values in the set A and set B boxes and click on the 'Go' button to check the final results.

What Are Sets

Let’s take an example to understand the meaning of sets. In a class of 70 students, 50 said they loved painting, 20 said they loved dancing.

The teacher wanted to find out how many students loved reading and painting, as well as those who did not have a hobby.

She grouped the students who had painting and dancing into groups called sets. Thus, you get to know what exactly the set is.

What is Included in the Set Calculator Theory?

Under the set finder theory, you will find the following:

  • intersection of two sets calculator

  • Set Union

  • Set Complement

  • Power set(Proper Subset)

  • Minus and Cross Product

  • Set identities discrete math

  • is two set Equal or not

  • Prove if any two expression are equal or not

  • Cardinality of a set

  • is subset of a set or is belongs to a set

Union of Sets

In mathematics, sets are referred to as an organized collection of objects and can be presented in the form of a set-builder or roster. In general, sets are displayed in curly brackets {}, for example, A = {1, 2, 3, 4, 5, 6, 7, 8} is a set. A set is denoted by a capital letter. The number of elements in the finite set is what we call as the cardinal number of a set. Various set operations can be described such as union, intersection, difference of sets. The symbol representing the union of sets is “U”.

What is a Union of Sets Calculator

Union of Sets Calculator is a free online tool which showcases the union of the given sets. The sets calculator tool not only makes the calculation faster but easier, and it also displays the union set in a fraction of seconds.

How to Use the Union of Sets Calculator?

A step-by-step process to use the union of sets calculator is as below:

Step 1: Insert the sets in the input field such as “{1, 2} union {3, 4}”

Step 2: Click the button “>>>>” to obtain the result

Step 3: Finally, the union of sets will be showcased in the new window

Solved Examples

Let’s consider an example to understand the concept of set calculator clearly.


If M = {1, 2, 3} and N = {5, 6,7}, then find M U N.



M = {1, 2, 3}

N = {5, 6, 7}

M U N = {1, 2, 3} U {5, 6,7}

= {1, 2, 3, 5, 6, 7}


In a school 200 students played basketball, 150 students played volleyball and 100 students played both. Evaluate how many students were there in the school?


Let us represent the number of students who played basketball as 

n(B)n(V) and

Number of students who played volleyball as 

n (V) n(S)

n (B)=200

n (V)=150

n (B∩V)=100

We are aware that,

n (B∪V)=n(B)+n(V)−n(B∩V)


N (F∪S) = (200+150) −100

N (F∪S) =350−100

N (F∪S) =250

Fun Facts

  • The cardinality of a set represents the number of elements in a set.

  • A Venn diagram can be used to create an accurate relationship between sets.

  • Each circle in a Venn diagram denotes a set.

FAQs on Set Calculator

Q1. What are the Different Properties of Operations of Sets?

Answer: The major properties on operations of sets are stated below.

  • Associative Property of Sets

For any three given sets M, N and O the associative property is described as,

(M∪N)∪O=M∪ (N∪O)

This implies that union of sets is associative.


This implies that intersection of sets is associative.

  • Commutative Property of Sets

For any two given sets M and N, the commutative property is described as,


This implies that union of two sets is commutative. 


This implies that intersection of two sets is commutative. 

  • Distributive Property of Sets

For any three given sets, M,N and O the distributive property is described as,

M∩ (N∪O)=(M∩N)∪(M∩O)

In this case, intersection is distributive over union of sets N and O.

M∪ (N∩O)=(M∪N)∩(M∪O)

In this case, the union is distributed over the intersection of sets N and O.

Q2. How to Express a Set in a Roaster Form?

Answer: In such a set representation, the elements of a set are supposed to be listed inside curly brackets {}.

For example,

Set A= {1, 2, 3, 4, 5, 6, 7}

Set B= {a, b, c, d, e, f, g}

You can also express the set in roster form calculator which will help you find the set and display the result in curly brackets only.

Q3. What is Mt by Cardinality of a Set?

Answer: The number of elements in a set typically describes the cardinality of a set. For a set C, cardinality is defined as n(C). 

For example,

SetC= {1, 2, 3, 4, 5, 6, 7}


n (C) =7