# Universal Set

## 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}

### 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.