Sets

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}