Understanding Set Concepts in Mathematics
Set theory is a fundamental concept in mathematics, defining sets as well-defined collections of objects with elements denoted by small letters. Properties of sets, operations on sets, and set representation using Venn diagrams are discussed. Georg Cantor's contributions to set theory and John Venn's Venn diagrams are highlighted, assisting in visualizing relationships between sets.
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Set Concepts Presented by Ms. Bobade Swati Bhaskar Department of Computer Sci. & IT Deogiri College, Aurangabad Maharashtra, 431 005 1
INDEX 1. Objectives 2. Definition of set 3. Properties of sets 4. Set theory 5. Venn Diagram 6. Set Representation 7. Types of Sets 8. Operation on Sets
Definition of set A set is a well defined collection of objects. Individual objects in set are called as elements of set. e. g. 1. Collection of even numbers between 10 and 20. 2. Collection of flower or bouquet.
Properties of Sets 1 Sets are denoted by capital letters. Set notation : A ,B, C ,D Elements of set are denoted by small letters. Element notation : For example SetA= {x,y,v,b,n,h,} a,d,f,g,
3 If x is element of A we can write as x A i.e x belongs to set A. 4. If x is not an element of A we can write as x A i.e x does not belong to A e.g If Y is a set of days in a week then Monday A and January A
5 Each element is written once. 6 Set of Natural no. represented by-N, Whole no by- W ,Integers by I, Rational no by-Q, Real no by- R 7 Order of element is not important. i.e set A can be written as { 1,2,3,4,5,} or as {5,2,3,4,1} There is no difference between two.
Set Theory Georg cantor a German Mathematician born in Russia is creator of set theory The concept of infinity was developed by cantor. Proved real no. are more numerous than natural numbers. Defined cardinal and ordinal no. Georg cantor
Venn Diagrams Born in 1834 in England. Devised a simple diagramatic way to represent sets. Here set are represented by closed figures such as : .2 .6 .8 John Venn
SetRepresentation There are two main ways of representing sets. Roaster method or Tabular method. Set builder method or Rule method
Roster or Listing method All elements of the sets are listed,each element separated by comma(,) and enclosed within brackets
Roster or Listing method All elements of the sets are listed,each element separated by comma(,) and enclosed within brackets { } e.g Set C= {1,6,8,4} Set T ={Monday,Tuesdy,Wednesday,Thursday, Friday,Saturday} Set k={a,e,i,o,u}
Rule method or set builder method All elements of set posses a common property e.g. set of natural numbers is represented by K= {x|x is a natural no} Here | stands for such that : can be used in place of | Set T={y|y is a season of the year} Set H={x|x is blood type} e.g.
Cardianility of set Number of element in a set is called as cardianility of set. No of elements in set n (A) e.g Set A= {he,she, it,the, you} Here no. of elements are n |A|=5 Singleton set containing only one elements e.g Set A={3}
Types of set 1. Empty set 2. Finite set 3. Infinite set 4. Equal set 5. Equivalent set 6. Subset Universal set
Equal sets Two sets k and R are called equal if they have equal numbers and of similar types of elements. For e.g. If k={1,3,4,5,6} R={1,3,4,5,6} then both Set k and R are equal. We can write as Set K=Set R
Empty sets A set which does not contain any elements is called as Empty set or Null or Void set. Denoted by or { } e.g. Set A= {set of months containing 32 days} Here n (A)= 0; hence A is an empty set. e.g. set H={no of cars with three wheels} Here n (H)= 0; hence it is an empty set.
