Set builder method or Rule method of Sets

For many sets it may not be possible;e to represent it in Roster form. For example” The set of ll natural numbers. If we try to write this in Roster form we will not be able to list out all the elements since the set is infinite. When our list cannot be completed, we use in such cases what is known as the Set builder method or Rule method for representing a set. Set builder method can be used in some cases where Roster method is also possible.

In this method we write a general element x and a ‘:’ meaning such that and state its property within brackets. (i) The set of all vowels in English alphabet is represented by

V = {x : x is a vowel in English alphabet}