# Ways of describing a set, writing sets, and examples

Describing a set or writing sets can be done in three main ways. A set is a collection of distinct objects of the same kind. Or a set is the collection of well-defined objects of the same kind. For example, a collection of flowers, or a set of even numbers. etc.

## Ways of describing a set and writing sets

Set may be described in three ways, this is explained below

• **Listing the members of the set:** a set can be described by listing the elements or members of that set. For example, P={2,4,6,8,10} or A ={1,3,5,…15} or D={September, April, June, November} or B={2,3,5,7,…}. In the last example, we have seen some three dots ending the members of set B. That three dots at the end means the members are infinite, we can continue listing the members of the set to infinity. There is always a clear pattern for you to know the members of that set. For instance, there are three dots in set A. That three dots means they are three missing members of the set which we can find because there is a clear pattern. So in the above example of set A will be; A={1,3,5,7,9,11,15}.

• **Giving a word description of its members**: a set can be described by giving a word description of its members or defining the properties of the set. For instance, the sets P, A, B, and D above can be written as

P= { Even numbers less than 12}

A={Odd numbers less than 17}

B={Prime numbers}

D= { Months with 30 days}

• **Using set builder notation**. In describing a set, we can use set builder notation to write the set. Let’s describe the sets above using set builder notation. For instance

P ={2,4,6,8,10} can be written in a set builder notation as P={1 < x < 12, where x is an even number}. Also, the set A={1,3,5,7,9,11,15} can be written in a set builder notation as N={1 ≤ x ≤ 15, where x is an odd number} or N={1 ≤ x < 17, where x is an odd number}.

Try this practice below

a). List the members of the following sets below

• A = { 10 < x < 26, where x is an even number}

• B is a set of months that begin with the letter J

• C is a set of vowels in the English Language.

For a definition of sets click here