## Definition of Empty Set

An **Empty Set** or **Null Set** may be defined as a unique set that has no elements in it. Therefore, the size of an **Empty Set** is zero (0) as it has no elements present. Also, the Cardinality of an **Empty Set** or **Null Set** is Zero (0).

An **Empty Set** sometimes is also referred to as a **Null set**.

## Symbol of Empty Set

The **Empty Set** or **Null Set** is denoted by the Greek letter ∅. An **Empty Set** or **Null Set** can also be represented by \{\}.

## Properties of an Empty Set

The Properties of an **Empty Set** are discussed below:

- The number of elements in an
**Empty set**is Zero (0). - An
**Empty Set**is a Subset of any set A. - The Union of an
**Empty set**with any set A is the set A itself.

Therefore, A ∪ \phi =A

- The Intersection of an
**Empty Set**with any set A is an**Empty Set**.

Therefore, A ∩ \phi =\phi

- The Cartesian product of an
**Empty Set**with any set A is an**Empty set**. - The only subset of an
**Empty Set**is the**Empty Set**itself.

## Example of Empty set

Some examples of **Empty set** is described below.

- The set of Prime Numbers between 7 and 11.

There are 3 numbers between 7 and 11. Those are 8, 9 and 10. None of these numbers is Prime. Therefore, the set of Prime Numbers between 7 and 11 is an **Empty Set** or **Null Set**.

- The set of Natural Number which are less than 1.

We know that the set of Natural Numbers starts from 1 and ends at +\infty. Therefore, there is no Natural Number that is less than 1. Hence, the set of Natural Numbers that are less than 1 is an **Empty Set** or **Null Set**.

- The Set of Prime Number which are less than 2.

Similarly, there is no Prime Number that is less than 2 as 2 is the smallest Prime Number. Therefore, the set of Prime Number which is less than 2 is an **Empty Set** or **Null Set**.

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