There are two methods to represent or write a set: 1. Listing Method/Roster Method: All elements of a set are listed within curly brackets, with each element written only once and separated by commas. 2. Rule Method/Set Builder Form: Instead of listing elements, a variable is used followed by a property that all elements of the set possess. This property describes the common traits of all elements in the set.

1. Vaibhav Zade, Navpratibha High School, Nagpur
Topic

2. Navpratibha Study Forum Vaibhav Zade, Navpratibha High School, Nagpur
There are two methods of
representing or writing a set
(i) Listing Method
or
Roster Method
(ii) Rule Method
or
Set Builder Form

3. 32
Vaibhav Zade, Navpratibha High School, Nagpur
We write all
the elements
of a set in
curly bracket.
Navpratibha Study Forum
Each of the
elements is
written only once
and separated by
commas.
The order of an
element is not
important but it is
necessary to write
all the elements of
the set.
In listing or roster
method , all elements of a
set are listed.
1

4. A = { M, A, T, H, E, M, A, T, I, C, S }A = { M, A, T, H, E, I, C, S }
Vaibhav Zade, Navpratibha High School, Nagpur
i) The set of all the letters in word ‘MATHEMATICS’.
Navpratibha Study Forum
Let see an example
ii) The set of odd numbers between 1 and 10
O = { 3, 5, 7, 9 } or O = { 9 ,7, 5, 3 }
iii) The Set of multiples of 7
B = { 7, 14, 21, 28, 35, 42, . . . . }
iv) The set of all vowels in the English alphabet
V = { a, e, i, o, u } v) The set of all natural factors of 42
F = { 1, 2, 3, 6, 7, 14, 21, 42 }

5. Vaibhav Zade, Navpratibha High School, NagpurNavpratibha Study Forum
Instead of
writing the
list of
elements,
we use a
variable.
In rule method or set
builder form, we describe
the set by indicating
properties of elements
321
Variable is
followed by
a vertical
line | or
colon :
Variable is
described
by the
common
property of
elements.
All the elements of a set possess a single common property
which is not possessed by any element outside the set.

6. Vaibhav Zade, Navpratibha High School, Nagpur
i) The set of all natural numbers between 1 and 10.
Navpratibha Study Forum
A = { x | x ∈ N, 1 < x < 10 }
set A is the set of all ‘x’ , such that, ‘x’ is a natural number,
between 1 and 10.
We read the set as follows :
Listing Method A = { 2, 3, 4, 5, 6, 7, 8, 9 }

7. Vaibhav Zade, Navpratibha High School, Nagpur
Set Builder form or Rule Method
Navpratibha Study Forum
Listing Method or Roster Method
S = { 1, 4, 9, 16, 25, 36, . . . } S = { x | x is a square of natural numbers }1.
or S = { x | x = n2 , n ∈ N }
2. Set of letters of word ‘PRINCIPAL’
A = { P, R, I, N, C, A, L } A = { y | y is a letter in word ‘PRINCIPAL’ }
3. C = { . . ., - 6, -4, -2, 2, 4, 6, . . . } C = { a | a ∈ I , a is an even number }
4. G = { - 7, 7 } G = { x | x ∈ I , x = 49 }

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