If we can definitely and clearly decide the objects of a given collection then that collection is called a set.
Generally the name of the set is given using capital letters A, B, C,....,Z
Ø The members or elements of the set are
shown by using small letters a, b, c, ...
Ø If a is an element of set A, then we write it as ‘a 
A’
and if a is not an element of set A then we write ‘a 
A’.
Now let us observe the set of numbers.
Ø N = { 1, 2, 3, . . .} is a set of
natural numbers.
Ø W = {0, 1, 2, 3, . . .} is a set of
whole numbers.
Ø I = {..., -3, -2, -1, 0, 1, 2, ...} is
a set of integers.
Ø Q is a set of rational numbers.
Ø R is a set of real numbers.
Methods of
writing sets
There are two methods of writing set.
(1) Listing method or
roster method
In this method, we write all the elements of
a set in curly bracket. 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.
e.g. the set of odd numbers between 1 and 10,
can be written as
as, A = {3, 5, 7, 9} or A = {7, 3, 5, 9}
If an element comes more than once then it is
customary to write that element only once. e.g. in the word ‘remember’ the
letters ‘r, m, e’ are repeated more than once. So the set of letters of this
word is written as A = {r, e, m, b}
(2) Rule method or set
builder form
In this method, we do not write the list of
elements but write the general element using variable followed by a vertical
line or colon and write the property of the variable.
e.g. A = {x ½ x 
N, 1 < x < 10 } and read as 'set A is the set of all ‘x’ such that
‘x’ is a
natural number between 1 and 10'.
e.g. B = { x | x is a prime number between 1 and 10}
set B contains all the prime numbers between
1 and 10. So by using listing method set B can be written as B = {2, 3, 5, 7}
Q is the set of rational numbers which can be
written in set builder form as Q ={ 
| p, q I, q 
0}
and read as ‘Q’ is set of all numbers in the
form 
such that p and q are integers where q is a
non-zero number.’
Illustrations : In the following examples
each set is written in both the methods.
Rule method or Set builder form
A = { x | x is a letter of the word ‘DIVISION’.}
B = { y | y is a number such that y2 = 9}
C = {z | z is a multiple of 5 and is less than 30}
Listing method or
Roster method
A = {D, I, V, S, O, N}
B = { -3, 3}
C = { 5, 10, 15, 20, 25}