Arham.pptx for maths sets class 12 beat for all

Ghhty

1. WELCOME TO SETS ARHAM

2. Representation of sets 1) Roster form = In this form we list all the members of set within curly brackets(). Example :- ( i ) the set of all even numbers in the roster form. A= { 2,4,6,8,10,12,14} (ii) The set of vowels in the english alphabet in the roster form. S = { a,e,i,o,u } ARHAM

3. 2) Set builder form = In this form we write a variable (x) representing any member of the set which followed by a colon ‘:’ then we write the property followed by each member and then combine all discription in braces. Example :- ( i )The set of A of all odd numbers less then 15 in set builder form. A = { x:x is an even natural numbers less then 15 (ii)The set of S of all vowels in the english alphabets. S = {x:x is the vowels} ARHAM

4. Kinds of sets 1)Empty set = a set which do not contain any element is called empty set. Example:- ( i ) {x:2x+11=3 and x is a natural numbers} (ii) collection of a natural numbers less then 1. (iii){x:x is an even prime number greater than 2} ARHAM 1)Empty set = a set which do not contain any element is called empty set. Example:- (i) {x:2x+11=3 and x is a natural numbers} (ii) collection of a natural numbers less then 1. (iii){x:x is an even prime number greater than 2}

5. Singleton set = a set that contain only one element is called singleton set. Example :- {0} {x:x is the capital of india .} {x:3x-1=8} Finite set = a set that contain limited number different element. Example :- S = {2,3,4,5,6,7} A = { a,e,i,o,u } ARHAM

6. Infinite set = a set that contain unlimited numbers of different element is called infinite set Example :- The set of even natural numbers {2,4,6………}. The set of odd number greater than 2. ARHAM

7. Cardinal number The number of different element in a finiote set is called a cardinal number . Example :- A= {1,9,8,7,5}, then n(A)=5 S={3,5,7,9}then n(S)=4 R = { a,e,I,o,u } then n(R)=5 NOTE = The cardinal number of empty set is zero and the cardinal number of infinite set is never defined and the cardinal number of singeleton set is 1… ARHAM

8. Some standards set of numbers ( i ) Natural numbers = The set of natural numbers is denoted by N. EXAMPLE :- N = {1,2,3,4,5…..} (ii) Whole numbers = The set of whole numbers is denoted by W. EXAMPLE :- W = {0,1,2,3,4,5,…} (iii) Integers = the set of all integers is denoted by I or Z. EXAMPLE:- I = {…..,-2,-1,01,2,3,4,…..} (iv) Rational numbers = Any number which can express in the form p/q where p,q are integers and q is not equal to 0. Denoted by Q ARHAM

9. SOME STANDARDS SET OF NUMBERS (v) Real numbers = All rational as well as irrational numbers are real numbers . Example :- -3,0,5,5/3,-7/6 (vi) Irrational numbers = The set of real numbers which are not rational and denoted by T . ((vii) Positive rational numbers = The set of positive rational numbers is denoted by +Q. (viii) Positive real numbers = The set of positive real numbers is denoted by +R . ARHAM

10. Subset Let A,B any two sets then A is called a subset of B if every member of A is also a member of B .we write it as A B Example :- A ={2,4,5,6} B ={1,2,3,4,5,6,7} You can easily see that every elements of A is the member of B then we can say that A is the subset of B. A B . ARHAM

11. Proper subset = A is called a proper subset of B if every member of A is also a member of B and there exists atleast one element in B which is not a member of A . ARHAM

12. Power set = The set formed by all the subsets of a given set A is called the proper set of A ,it is denoted by P(A). EXAMPLE :- A = {1,2},then P(A) = {0,{1},{2},A}. Universal set = A set that contains all the elements under consideration in a given problem is called Universal set . EXAMPLE :- ( i ) For A = { b,c,g,m,u },universal set may be {x:x is a letter in English alphabet }. ARHAM

13. Venn Diagram Most the ideas about set and the various relationships between them can be visualised by means of geometric figures known as Venn Diagram. Usually the universal set is denoted by a rectangle and its subsets by enclosed curves within the rectangle ,such as circles ,ovals etc. EXAMPLE :- The set A of factors of 12 {1,2,3,4,6,12} U ={1,2,3,4,5,6,7,8,9,10,11,12} D ARHAM

14. Diagram 1 2 12 3 4 6 U 5 7 8 9 10 11 A ARHAM

15. Operation on sets Union of two sets The union of two sets of A and B written as A U B is the set consisting all the elements belong to A or B or both. AUB = {x:x E A or x E A} EXAMPLE :- Let A ={1,2,3,4,5} and B ={1,3,5,7,9},then AUB = {1,2,3,4,5,7,9}. (ii) Let A ={ a,b,c,d,e,i } and B ={ c,a,e,i },then AUB = { a,b,c,d,e,i } ARHAM

16. Union set diagram AUB(shaded area) ARHAM

17. Intersection of two sets The intersection of two sets A and B written as A U B ARHAM