# What is Sets in Mathematics – Methods to write a Set

Here, you will learn what is sets in mathematics and different methods to write a set with examples.

Let’s begin –

## What is Sets in Mathematics ?

A set is a collection of well defined objects which are distinct from each other.

Set are generally denoted by capital letters A, B, C, ….. etc. and the elements of the set by a,b,c …..etc.

If a is an element of a set A, then we write a $$\in$$ A and say a belongs to A.

If a does not belong to A then we write a $$\notin$$ A.

Example : The collection of first five prime natural numbers in a set containing the elements 2,3,5,7,11.

Some important number sets

N = Set of all natural numbers = {1, 2, 3, ….}

W = Set of all whole numbers = {0, 1, 2, 3, ….}

Z = Set of all integers = {…..-3, -2, -1, 0, 1, 2, 3,….}

Q = the set of all rational numbers

R = the set of all real numbers

## Methods to write a set

(i) Roster Method :

In this method a set is described by listing elements, separated by comma and enclose then by curly brackets.

Example : The set of vowels of English Alphabet may be described as {a, e, i, o ,u}.

(ii) Set builder Form :

In this case we write down a property or rule p which gives us all the element of the set A = {x : P(x)}

Example : A = {x : x $$\in$$ N and x = 2n for n $$\in$$ N}

i.e. A = {2, 4, 6, …..}