# Empty Set

## 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.