Set theory.pptxyz1234567891012345678901w

Ppt on set theory

1. Set theory By:- Raj P rasad Roll No:-31 SECTION:-A

2. T opics History of set Definition of set Methods of representing set Types of set Operation on set

3. History of set The theory of set was given by German mathematician “Georg Cantor” ( 1845-1981). He first encountered sets while working on “Problems on Trigonometrics series” . Sets are being used in mathematics problem since they were discovered.

4. Definition of set Set - A collection of well defined elements are called set . Well defined means common relation between collection of element Ex. A={1,2,3,4,5,....}

5. METHODS FOR REPRESENTING SET Roster Method – In this method we write collection of element directly in the mid bracket and seprate them by comma. A={1,2,3,4,5} 2. Set Builder method – In this method we write comman relation between collection of element in the mid bracket. A={ x:x is a real number}

6. Types of set 1. Null set – A set containing no element in it and it is denoted by ‘Φ ’. Ex-A={} 2. Singleton set – A set containing only 1 element called singleton set . Ex-A={3} 3. Pair of set – A set containing only 2 elements called pair of set. Ex-A={2,6} 4. Finite set - Any set is called finite set if it has finite numbers of elements . Ex-A={4,6,8,10,12,14} 5. Infinite set - Any set is called infinite set if it has infinite numbers of elements. Ex-A={set of all natural numbers} 6. Equal Set – If all element of 2 set are equal then it is called equal set .

7. 7. Equivalent set - If cardinal number of set is same are called equivalent set. Eg : C={4,5,6} D={ x,y,z } N(C)=n(D)=3 8. Multiset – A set containing more than elements is called multiset. 9. Subset – if set A and B are 2 sets then set A is said to be a subset of B if all elements of set b is present in set A. Eg : A={1,2,3,4,5,6} B={2,4,6} Then, set B ⊆ set A . 10. proper subset – set A is considered to be a proper subset of set B if set B contains at least at least one element that is not present in set A. Eg : A={12,24} and B={12,24,36} then, A is proper sub set of B.

8. OPERATION OF THE SET   1.Union (∪): Let A and B be two sets then the set of all those elements lies in A or B or both is called union of A and B. It is denoted by AUB. (AUB) = {x: X∈A or X∈B} 2. Intersection(∩) : Let and B be two sets then the set of all common elements in A and B is called intersection of A and B. It is denoted by (A∩B). (A∩B) = {x: x∈A and x∈B } 3.Difference(A-B) – Let A and B be two sets then the set of all those elements of B which doesn’t lies in A is called difference of A and B Eg : A={1,2,3,4} B={3,4} A-B = {1,2}

9. Some important sets 1 .Symmetric difference – if A and B be two sets then the set of all those elements lines in A or B but not in both is called symmetric difference. It is denoted by AΔB. AΔB = (A-B)U(B-A) 2 .Universal set – Any set is called universal set if it super set if it all the set. 3 .Super set – Let A and B be two sets and all the elements of set B lies in set A then set A is called super set of set B. 4 .Complement of set – Let U be the universal set and A be any set then U-A is called complement of set A. It is denoted by A’ .

10. Thank you