1.2 Set and their Representations

Set: A set is a well-defined collection of objects. 

(i) Objects, elements and members of a set are synonymous terms.

(ii) Sets are usually denoted by capital letters A, B, C, X, Y, Z, etc.

(iii) The elements of a set are represented by small letters a, b, c, x, y, z, etc.


If a is an element of a set A, or “a belongs to A” then the Greek symbol (epsilon) is used to denote the phrase belongs to’. 

 ∈ (epsilon)   =  belongs to

Thus, we write a A         [element a belongs to set A]

 If ‘b’ is not an element of a set A, we write -

 b A and read b does not belong to A”.


Set representation methods:- 

(i) Roster or tabular form

(ii) Set-builder form.

 Roster form: - All the elements of a set are listed, the elements are being separated by commas (,) and are enclosed within braces { }.

 For example, 

The set of all even positive integers less than 7 = {2, 4, 6}  

The set of all natural numbers which divide 42 = {1, 2, 3, 6, 7, 14, 21, 42}

The set of all vowels in the English alphabet = {a, e, i, o, u}

The set of odd natural numbers = {1, 3, 5, . . .}

Note:- The dots tell us that the list of odd numbers continue indefinitely.

Note:- In roster form, the order in which the elements are listed is immaterial.

Note:- while writing the set in roster form an element is not generally repeated, i.e., all the elements are taken as distinct.

Set-builder form: - All the elements of a set possess a single common property which is not possessed by any element outside the set.

 For example,

 In the set {a, e, i, o, u}, all the elements possess a common property (each of them is a vowel) and no other letter possess this property.


Denoting this set by V, we write V = {x : x is a vowel in English alphabet}    (set-builder form)


A = {x: x is a natural number and 3 < x < 10}         (set-builder form)


Here “A is the set of all x such that x is a natural number and x lies between 3 and 10.”

Hence, the numbers 4, 5, 6, 7, 8 and 9 are the elements of the set A.

Roster Form (RF)

Set Builder Form (SBF)

    A = {1, 2, 3, 6, 7, 14, 21, 42}

   A= {x : x is a natural number which divides 42}

    V = {a, e, i, o, u}

   V= {y : y is a vowel in the English alphabet}

    B = {1, 3, 5, . . .}

   B = {z : z is an odd natural number}

Last modified: Friday, 24 June 2022, 8:18 PM