Welcome to Priya Mathematics  Class 

 

 BASIC CONCEPTS  OF SETS ....

1) what is the sets  ?

ans)  A well define collection of object's(element's) . Arrangement of element does not matter .

 let's understand with example 

1st example 

A={ a, e, i ,o, u} . you can also write  A = { u, o, i, a, e }

here "A" represent the set's and within curly braces ,, that's all element are element of set's represent by small letters .

 

2) What is element ?  

 An object's in a set's are called it's member or Element's of set's . 

In a first example a, e , i ,o ,u all are the element of set's .  

3) Example of set's 

1. The collection of all vowel in English alphabet .

Example :-  A = { a,e,i,o,u}

2) The collection of natural numbers less then 10 .

3) Collection of all prime numbers less then 20, is the set's .

many of other example which are specific and universal define ,, that's all are   set's .

Poor people , handsome boy , intelligent boy or girl , beautiful girl , rich man ,, that's all are not example of set's . Because these all are not specific . 

 

1. Sets of all Natural number denoted by :-  N
2. Sets of all Integer denoted by :-                  Z
3.  Sets of all Rational number denoted by  :-  Q
4. Sets of all Real number denoted by  :-        R 
5.  Sets of all Positive integers denoted by :-  z+ 

       Sets of all positive Rational  denoted by  :-   Q  

 

Q) What is proper subsets ?

 Ans)   We called ,, Proper subset of a sets when every element of  A is also an element of B ,, but B is not belong to element of sets A .

   Example :-  let A= { 3,  5 ,9} 

                        and B =  { 3 ,4 , 5 , 6 , 7 , 8 ,9 }

      Thus every element of A is an element of B  .

      So, A is proper subset of B . and it's denoted by    :- A⊂B

               This means A is proper subset of B , but A is not equal to B . 

 

TYPE OF SETS  

1) EMPTY SET  :- NO ELEMENT IN THIS SET .

2) SINGLETON SET :-SINGLE ELEMENT IN THIS SET

3 )FINITE SET :- IT CAN BE LISTED BY NATURAL NUMBER .

4) INFINITE SET :- IT CANNOT BE LISTED BY NATURAL NUMBER .

6)EQUIVALENT SET :- NUMBER OF ELEMENT ARE SAME .

7) EQUAL SET :- EQUAL ELEMENT IN THIS SET .