Introduction of set

Jun 25, 2018Download as pptx, pdf3 likes506 views

In this presentation we will learn the concept of set theory ,learn some known sets and also know method to express the set in which we will see Roster form and set builder form . For more concept we take examples. Introduction of set introduction of sets introduction of set theory introduction of sets in mathematics introduction of sets introduction of set math introduction of set in math introduction of sets in math

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

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

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
 
  
 

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

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.

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
 
    
 

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 }

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.

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Introduction of set

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

Introduction of set

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