Empty Set (Null or Void Set) in Math – Symbol and Examples

Here you will learn what is an empty set in math, its symbol and definition with examples.

Let’s begin –

What is the Empty Set in Math ?

Definition : A set is said to be empty set if it has no element. It is also called null or void set.

It is denoted by the symbol $\phi$.

In Roster method, $\phi$ is denoted by { }.

It follows from the definition that a set A is an empty set if the statement x $\in$ A is not true for any x.

Example 1 : { x $\in$ R : $x^2$ = -1 } = $\phi$

Example 2 : The set A given by A = { x : x is an even number greater than 2 } is an empty set because 2 is the only even prime number.

A set consisting of atleast one element is called a non-empty or non-void set.

Note : If A and B are any two empty sets, then x $\in$ A iff (if and only if) x $\in$ B is satisfied because there is no element x in either A or B to which the condition may be applied. Thus A = B. Hence, there is only one empty set and we denote it by $\phi$.

Note : The power set of an empty set has only one element i.e. P(A) = {$\phi$}.