Hello Vanadana,

Lets take an example of set of natural numbers less than 6.

In roster form, A = {1, 2, 3, 4, 5} 

and in set-builder form, A = {x : x is a natural number less than 6}

Lets study some examples inorder to understand how to represent set in set-builder form

We look at two things

1. What type of number is x , is it integer, real number or whole number?
2. A pattern in the given set

For example:

A = {1, 4, 9, 16, 25, . . . }

A = {1², 2², 3², 4², 5², . . . }

Note :- 1, 2, 3, 4, 5 are all natural numbers

and 1, 4, 9, 16, 25 are their squares

Hence, we may write the set A as

A = {x : x is the square of a natural number}

or A = {x : x = n², where n ∈ N}

For more questions on set-builder form, please check depiction of sets in set-builder form.

Please comment for any further queries.