Chapter 1. Sets
#Definition of sets:- A set is well defined collection of object.
By well defined we mean there should be no Ambiguilty regarding the inclusion and exclusion of the
object.
Q.which of the following statement is well defined ?
1.collection of even number An :- well defined
2.collection of best teacher. An:-not well defined
3.collection of most talented writers of india. An:- not well defined
4.collection of all the vowels in English alphabet. An:- well defined
5.collection of all roots of equation (x2+5x-6=0) An:- well defined
# Representation of sets
There are two methods for representing a set.
1. Roster form or tabular method :
All the elements belonging to the set are writing in Curly brackets and separated by commas
If A is the set of days of a week,then
A = { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
2. Set builder method :
we use the definition,which is satisfied by all the elements of set.
In above example set A may be written as A={X:X is a day of week}
#notation of set of different number.
1.set of all natural number N={1,2,3,....}
2.set of all integers Z to I ={...,-3,-2,-1,0,1,2,3,...}
3.set of non zero integers ={...,-3,-2,-1,0,1,2,3,...}
, 4.set of all rational numbers
Q = {x:x = p/q, where p and q relatively prime integers and q ≠ 0}
5.set of real numbers is denoted by R
6.set of complex numbers is denoted by c
# cardinal number
The number of distinct elements in a set A is denoted by n(A) and it is known as cardinal number of
set A.
Two finite sets A and B are equivalent if their cardinal number are same.
Example:A={X € z and X2 +5x+6=0}
So ,A={2,3}
So,n(A)=2
# Type of set
1. Null set or void set or empty set:
A set having no element is called as null set or empty set or void set.it is denoted by ϕ or { } . The null
set is the subset of every set.
Example:
Set of even prime numbers less than 2.
Set of natural number strictly lying between 5 and 6 .
A = {X:x ∈ N,5 ‹ x ‹ 6 } = ϕ
2.Finit set :
A set which is empty or consists of a definite number of elements.
Example:
Set of all natural number less than 6 = {1,2,3,4,5}
3.Infinit sets:
#Definition of sets:- A set is well defined collection of object.
By well defined we mean there should be no Ambiguilty regarding the inclusion and exclusion of the
object.
Q.which of the following statement is well defined ?
1.collection of even number An :- well defined
2.collection of best teacher. An:-not well defined
3.collection of most talented writers of india. An:- not well defined
4.collection of all the vowels in English alphabet. An:- well defined
5.collection of all roots of equation (x2+5x-6=0) An:- well defined
# Representation of sets
There are two methods for representing a set.
1. Roster form or tabular method :
All the elements belonging to the set are writing in Curly brackets and separated by commas
If A is the set of days of a week,then
A = { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
2. Set builder method :
we use the definition,which is satisfied by all the elements of set.
In above example set A may be written as A={X:X is a day of week}
#notation of set of different number.
1.set of all natural number N={1,2,3,....}
2.set of all integers Z to I ={...,-3,-2,-1,0,1,2,3,...}
3.set of non zero integers ={...,-3,-2,-1,0,1,2,3,...}
, 4.set of all rational numbers
Q = {x:x = p/q, where p and q relatively prime integers and q ≠ 0}
5.set of real numbers is denoted by R
6.set of complex numbers is denoted by c
# cardinal number
The number of distinct elements in a set A is denoted by n(A) and it is known as cardinal number of
set A.
Two finite sets A and B are equivalent if their cardinal number are same.
Example:A={X € z and X2 +5x+6=0}
So ,A={2,3}
So,n(A)=2
# Type of set
1. Null set or void set or empty set:
A set having no element is called as null set or empty set or void set.it is denoted by ϕ or { } . The null
set is the subset of every set.
Example:
Set of even prime numbers less than 2.
Set of natural number strictly lying between 5 and 6 .
A = {X:x ∈ N,5 ‹ x ‹ 6 } = ϕ
2.Finit set :
A set which is empty or consists of a definite number of elements.
Example:
Set of all natural number less than 6 = {1,2,3,4,5}
3.Infinit sets:
