# Set builder form definition in math explained

Learn and know what is the meaning of set builder form in sets chapter in mathematics. We know that to represent any set we have three methods. In the three methods, set builder form is one of them. Set builder form is also called as rule method.

The three methods to represent any set are 1. Descriptive form (this will be in sentence form) 2. Roster form or list form (all the elements in the set will be listed) and 3. Set builder form i.e. rule method. Now we will learn about the third form i.e. rule form.

## The definition of set builder form as follows:

If the elements of any set is represented by a rule or by its common property then that representation is said to be set builder form or rule form.

Examples:

D = {1, 8, 27, 64, 125, 216} is in roster form.

D = {x: x = ${ s }^{ 3 }$, s∈N and s <7}, in the set D, all the elements are having a common property i.e. all they are cube numbers. So we represented that property.

H = {0, 2, 4, 6, 8, 10, 12, 14, 16}

H = {x: x = 2s, s∈W, s<9} all the elements which are listed in the set H are even numbers or we also can say they are multiples of 2. So the general form of even numbers or the multiples of 2, we represented as 2s.

K = {5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49}

K = {x: x = 4t + 1, t∈N, t<13} all the elements which are listed in the set K are one more than the multiples of the number 4. So that property represented as 4t + 1.

Hope that now you know how to write any given set in rule method.