Lesson1:
Set:
A set is collection of well define object. Sets are usually denoted by capital letter ,
such as A, B, C, …… P, Q, R and so on.
Eg: it is a
collection of even number less than 10. Here, the statement ‘ even numbers less than 10’
defines the distinct and distinguishable object s which are to be
included I n the collection.
Method of describing a set:
A set can be described by the
following three methods:
1.
Description
method :
W={whole
numbers less than 10}
2.
Listing method:
W={0, 1, 2,
3, 4, 5, 6, 7, 8, 9 }
3.
Set-building method:
W={x; x is
a whole number less than 10 }
Cardinal number of sets:
The number of elements contained by
a set is known as its cardinal number
. its denoted by n{ }. For example in A={ 1,3,5,7,9}, its cardinal number n(A) =5.
Type of Sets :
On the basis of the number of
element s contained by sets, they are classified into the following different
types.
I.
Empty of null set:
a set is
said to be a empty or a null set if it
does not contain any elements. Its denoted
by { } of f(phi) . For
example:
A= {natural
numbers between 5 and 6}
II.
Unit or singleton set:
A set is
said to be unit or singleton set if it contains only one element. For example:
P= { even
number between 5 and 7}
III.
Finite and Infinite sets:
A set said
to be a finite set if it contains a finite elements. On
other hands, if a set contains infinite numbers, it is called in finite
set. For example:
A={1, 2, 3,
4, 5, 6, 7, 8, 9,} is a finite set
B={1, 2, 3,
4, 5, 6, 7, 8, 9,…......} is a infinite
set.
Set operations
There are four fundamental set
operations. They are:
1) Union of sets:
When the
elements of two or more sets are listed together in a single set, It is called the union of these sets .
For example:
If
A={1,3,5,7,9} and B={2,3,4,5},
The union
of set A and B = {1, 2, 3, 4, 5, 7, 9}
It’s
denoted by AÈB={1, 2, 3,
4, 5, 7, 9}
2) Intersection of sets
When the
common element of two or more sets are listed in separate set , its called
intersection of set s. For example:
If
A={1,3,5,7,9} and B={2,3,4,5},
The union
of set A and B = {3, 5}
It’s
denoted by AÇB= {3, 5}
3) Difference of sets
The
difference of two sets A and B denoted
by A-B is the set of all elements
contained only by A but not by B. For
example
If
A={1,3,5,7,9} and B={2,3,4,5},
The
difference of set A and B = {1, 7, 9}
It’s
denoted by A-B= {1, 7, 9}
4) Complement of sets
If a set A
is the sub set of universal set U, then
its complement denoted by A¢ is the set which is formed due to the
difference of U and A, i.e.(U-A). for
example:
If U ={1,
2, 3, … … , 10} and A={2, 5, 8, 9}
The
complement of A=U-A= {1, 3, 4, 6, 7, 10}
It is
denoted by A¢ = {1, 3,
4, 6, 7, 10}
