# Set Builder Form Method

In the set builder form method, all the elements of the set, must possess a single property to become the member of that set. In this rule method, the element of the set is described by using a symbol ‘x’ or any other variable followed by a colon ':' and then we write the property possessed by the elements of the set and enclose the whole description in braces '()'. Here 'colon' stands for ‘such that’ and braces stand for ‘set of all'.

## Rule Method

In rule method, the formula is written within the pair of brackets so that the set is well defined.

###### Example

Let us consider 'P' is a set of counting numbers greater than 10.
The set P in set-builder form is written as :

**P = {x : x is a counting number and greater than 10} **

or

**P = {x | x is a counting number and greater than 10}**

The above set-builder notation property is enclosed as the whole description as, **P is the set of elements x such that x is a counting number and is greater than 10.**