Table of Contents

## Definition of Universal Set

An **Universal Set** of any set say A or B, may be defined as the set, that contains all the elements of set A or B, including its own elements without repetitions.

## Symbol of Universal Set

There is no standard notation for the **Universal Sets**, but the most commonly used symbols for **Universal Sets** are V, U, and ξ.

## Explanation of Universal Set

To understand the concept of **Universal Set**, let us consider a set A that consists of 4 elements as,

A = \{1, 2, 3, 4\}

And, let us consider another set B which also consists of 4 elements as,

B = \{9, 10, 11, 12\}

Then, the **Universal Set** U, will consist of all the elements present in set A and set B and also its own elements. Therefore, an **Universal Set** of the given two sets A and B will be,

U = \{1, 2, 3, 4, 9, 10, 11, 12, 13, 14\}

However, it is not necessary for an **Universal Set** to have its own elements. It can also be formed only by the elements of the sets A and B.

## Venn Diagram of Universal Set

The figure below shows the **Venn Diagram** for **Universal Set** of the above two sets A and B.

## Solved Examples on Universal Sets

### Let A={a, b, c, d} and C={d, r, s, t}. Find the universal set?

The universal set *U* will contain all the elements of set *A* and set *B*.

Therefore, Universal set, *U={a, b, c, d, r, s, t}*

### Find the universal set of the three sets A={1, 2, 4}, B={5, 6, 3} and C={9, 7, 10}?

The universal set *U* will have all the elements of *A, B* and *C*.

Therefore, *U={1, 2, 3, 4, 5, 6, 7, 9, 10}*

## Frequently Asked Questions (FAQ)

### What does Universal Set mean?

An **Universal Set** of any set say* A* or *B*, is the set, that contains all the elements of set* A* or *B*, including its own elements without repetitions.

### What is a universal set in math?

An **Universal Set** of any set say* A* or *B*, is the set, that contains all the elements of set* A* or *B*, including its own elements without repetitions.

### What is the difference between universal set and subset?

The universal set *U* of any set* A* is the set that contains all the elements of *A* including its own elements.

However, Set *A* is called the subset of *B* if all the elements of set *A* is present in the set *B*.

### What is the cardinality of a Universal Set?

The Cardinality of a Universal Set is the number of elements present in the set. Let* U* is a universal set of any set and it contains *15* elements, then the Cardinality of the set *U* is, *n(U)=15*.

### What is Universal Set example?

Example of Universal Set:

Let us consider two sets *A* and *B* such that,

*A={a, b, c, d}* and *B={e, f}*

Then one of the universal set *U* of *A* and *B* will be,

*U={a, b, c, d, e, f}*

### What is the difference between superset and universal set?

Superset: Set A is called Superset of B if all the elements of B is present in A.

Universal Set: An Universal set is the set that contains all the elements or sets that can be formed.

**Read Also**

Hi, my name is **Abdur Rohman**. By profession, I am an **Electrical Engineer**. I am also a part time **Teacher**, **Blogger** and **Entrepreneur**. The reason for starting this Website or Blog is mainly because **I love teaching**. Whenever I get time, I teach students/aspirants irrespective of their class or standards. More Info