The document provides an introduction to sets, defining them as collections of well-defined objects expressed within braces and represented by capital letters. It discusses methods to express sets, including roster form and set builder form, along with examples of known sets such as natural, integer, rational, and real numbers. Additional notes cover concepts like singleton and empty sets.

2. We have to learn:
 Introduction to Set
 Some known sets
 Method to express set
 Some example

3. Set
 Set is collection of well-defined object or element.
 Element may be any number , alphabets etc.
 It is expressed by enclosing its members within
a pair of braces.
 Set is always represented by capital letter.
Example :
A = { a , b , c }
Set
Elements
Enclosed by pair of braces

4. Some known sets
 N = The set of all natural numbers.
N = { 1 , 2 , 3 , …….}
 Z = Set of all integer numbers.
Z = { …. -2 , -1 , 0 , 1 ,2 , ….}
 R = Set of all real numbers.
 Q = set of all rational numbers.
Q = | ,
p
p Z q N
q
 
  
 

5. Method of expressing a set
It can be expressed by two ways:
1. Listing Method ( Roster Form )
2. Property Method ( set Builder Form )

6. Listing Method
 The element of a set can be simply separated by commas.
Example :
A = { 1 ,2 , 3 }
 In this method no element is repeated.
Example :
The set of letter of word BANANA is written by ,
S = { A , B , N }
 Order not important.

7. Property Method
 A set is expressed by some common characteristics property
P(x) of element x of the set.
Notation:
Set = { x | P(x) } = { x | the property of x }
Read as the set of all x possessing given property P(x).
| | ,
p
Q x x p Z q N
q
 
    
 

8. Some Examples
 Write a following sets in Roster Form:
1. { x | x is a natural number less than 10 }
Roster form : A = { 1 , 2 , 3 , … , 9 }
2. 2
{ | 5 6 0, }x x x x R   
2
2
5 6 0
6 6 0
( 6) 1( 6) 0
( 1)( 6) 0
,
1
6
x x
x x x
x x x
x x
Then
x
x
  
   
   
  
 

Roster Form:
Set A = { -1 , 6 }

9. Notes
1. A set contains only one element called Singleton.
A = { 2 }
2. If set which does not contain any element is called
Empty Set or Null Set .
A = { } or 
3. A set which does not empty is called Non-Empty Set.

10. Thank
You