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Set concepts

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Malti Aswal

The document defines set concepts and their properties. It explains that a set is a collection of distinct objects, called elements. Properties discussed include how sets are denoted, elements belong or don't belong to sets, order doesn't matter, and counting each element once. It also covers set theory, Venn diagrams, ways to represent sets, types of sets (empty, finite, infinite), equal sets, subsets, cardinality, and operations like intersection, union, difference, and complement of sets. Examples are provided to illustrate each concept.

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Set Concepts
Introduction
Shaan Education societys Guardian college of education Technology based lesson
NAME OF THE STUDENT: MALTI RAI NAME OF GUIDE: MRS NILOFER MOMIN NAME OF THE INCHARGE: MRS LEENA CHOUDHR Y
SUBJECT: Mathematics UNIT : Set concepts STANDARD: IX
INDEX Objectives Definition of set Properties of sets Set theory Venn Diagram Set Representation Types of Sets Operation on Sets
Understanding set theory helps people to see things in terms of systems organize things into groups begin to understand logic Objectives
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 : a,d,f,g, For example SetA= {x,y,v,b,n,h,}
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 : John Venn .a .i .g .y .2 .6 .8
Set Representation 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 | e.g. Set T={y|y is a season of the year} Set H={x|x is blood type}
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 Empty set Finite set Infinite set Equal set Equivalent set 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.
Finite set Set which contains definite no of element. e.g. Set A= { , , , } Counting of elements is fixed. Set B = { x|x is no of pages in a particular book} Set T ={ y|y is no of seats in a bus}
Infinite set A set which contains indefinite numbers of elements. Set A= { x|x is a of whole numbers} Set B = {y|y is point on a line}
Subset Sets which are the part of another set are called subsets of the original set. For example, if A={3,5,6,8} and B ={1,4,9} then B is a subset of A it is represented as B A Every set is subset of itself i.e A A Empty set is a subset of every set. i.e A .3 .5 .6. .8 .1 .4 .9 A B
Universal set The universal set is the set of all elements pertinent to a given discussion It is designated by the symbol U e.g. Set T ={The deck of ordinary playing cards}. Here each card is an element of universal set. Set A= {All the face cards} Set B= {numbered cards} Set C= {Poker hands} each of these sets are Subset of universal set T
Operation on Sets Intersection of sets Union of sets Difference of two sets Complement of a set
Intersection of sets Let A and B be two sets. Then the set of all common elements of A and B is called the Intersection of A and B and is denoted by A B Let A={1,2,3,7,11,13}} B={1,7,13,4,10,17}} Then a set C= {1,7,13}} contains the elements common to both A and B Hence AB is represented by shaded part in venn diagram . Thus AB={x|x A and x B}
Union of sets Let A and B be two given sets then the set of all elements which are in the set A or in the set B is called the union of two sets and is denoted by AUB and is read as A union B Union ofSet A= {1, 2, 3, 4, ={0, 2, 4, 6 } 5, 6}and Set B
Difference of two sets The difference of set A- B is set of all elements of A which does not belong to B. In set builder form difference of set is:- A-B= {x: x A x B} B-A={x: x B x A} e.g SetA ={ 1,4,7,8,9} Set B= {3,2,1,7,5} Then A-B = { 4,8,9}
Disjoint sets Sets that have no common members are called disjoint sets. Example: Given that U= {1,2,3,4,5,6,7,8,9,10} setA={1,2,3,4,5} setC={ 8,10} No common elements hence set A and are disjoint set.
Summarisation Definition of set andProperties of sets Set theory Venn Diagram Set Representation Types of Sets
Home work 1 Write definition of set concepts. 2 What is intersection and union of sets. 3 Explain properties of sets with examples.
Applications A set having no element is empty set. ( yes / no ) 2.A set having only one element is singleton set. ( yes / no ) 3.A set containing fixed no of elements.{ finite / infinite set ) 4.Two set having no common element. ( disjoint set / complement set )
Yes your answer is right
No is wrong your answer
Yes your answer is right
No your answer is wrong
Yes your answer is right
No your answer is wrong
Yes your answer is right
No your answer is wrong

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Set concepts

  • 3. Shaan Education societys Guardian college of education Technology based lesson
  • 4. NAME OF THE STUDENT: MALTI RAI NAME OF GUIDE: MRS NILOFER MOMIN NAME OF THE INCHARGE: MRS LEENA CHOUDHR Y
  • 5. SUBJECT: Mathematics UNIT : Set concepts STANDARD: IX
  • 6. INDEX Objectives Definition of set Properties of sets Set theory Venn Diagram Set Representation Types of Sets Operation on Sets
  • 7. Understanding set theory helps people to see things in terms of systems organize things into groups begin to understand logic Objectives
  • 8. 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.
  • 9. 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 : a,d,f,g, For example SetA= {x,y,v,b,n,h,}
  • 10. 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
  • 11. 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.
  • 12. 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
  • 13. Venn Diagrams Born in 1834 in England. Devised a simple diagramatic way to represent sets. Here set are represented by closed figures such as : John Venn .a .i .g .y .2 .6 .8
  • 14. Set Representation There are two main ways of representing sets. Roaster method or Tabular method. Set builder method or Rule method
  • 15. Roster or Listing method All elements of the sets are listed,each element separated by comma(,) and enclosed within brackets
  • 16. 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}
  • 17. 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 | e.g. Set T={y|y is a season of the year} Set H={x|x is blood type}
  • 18. 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}
  • 19. Types of set Empty set Finite set Infinite set Equal set Equivalent set Subset Universal set
  • 20. 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
  • 21. 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.
  • 22. Finite set Set which contains definite no of element. e.g. Set A= { , , , } Counting of elements is fixed. Set B = { x|x is no of pages in a particular book} Set T ={ y|y is no of seats in a bus}
  • 23. Infinite set A set which contains indefinite numbers of elements. Set A= { x|x is a of whole numbers} Set B = {y|y is point on a line}
  • 24. Subset Sets which are the part of another set are called subsets of the original set. For example, if A={3,5,6,8} and B ={1,4,9} then B is a subset of A it is represented as B A Every set is subset of itself i.e A A Empty set is a subset of every set. i.e A .3 .5 .6. .8 .1 .4 .9 A B
  • 25. Universal set The universal set is the set of all elements pertinent to a given discussion It is designated by the symbol U e.g. Set T ={The deck of ordinary playing cards}. Here each card is an element of universal set. Set A= {All the face cards} Set B= {numbered cards} Set C= {Poker hands} each of these sets are Subset of universal set T
  • 26. Operation on Sets Intersection of sets Union of sets Difference of two sets Complement of a set
  • 27. Intersection of sets Let A and B be two sets. Then the set of all common elements of A and B is called the Intersection of A and B and is denoted by A B Let A={1,2,3,7,11,13}} B={1,7,13,4,10,17}} Then a set C= {1,7,13}} contains the elements common to both A and B Hence AB is represented by shaded part in venn diagram . Thus AB={x|x A and x B}
  • 28. Union of sets Let A and B be two given sets then the set of all elements which are in the set A or in the set B is called the union of two sets and is denoted by AUB and is read as A union B Union ofSet A= {1, 2, 3, 4, ={0, 2, 4, 6 } 5, 6}and Set B
  • 29. Difference of two sets The difference of set A- B is set of all elements of A which does not belong to B. In set builder form difference of set is:- A-B= {x: x A x B} B-A={x: x B x A} e.g SetA ={ 1,4,7,8,9} Set B= {3,2,1,7,5} Then A-B = { 4,8,9}
  • 30. Disjoint sets Sets that have no common members are called disjoint sets. Example: Given that U= {1,2,3,4,5,6,7,8,9,10} setA={1,2,3,4,5} setC={ 8,10} No common elements hence set A and are disjoint set.
  • 31. Summarisation Definition of set andProperties of sets Set theory Venn Diagram Set Representation Types of Sets
  • 32. Home work 1 Write definition of set concepts. 2 What is intersection and union of sets. 3 Explain properties of sets with examples.
  • 33. Applications A set having no element is empty set. ( yes / no ) 2.A set having only one element is singleton set. ( yes / no ) 3.A set containing fixed no of elements.{ finite / infinite set ) 4.Two set having no common element. ( disjoint set / complement set )
  • 34. Yes your answer is right
  • 35. No is wrong your answer
  • 36. Yes your answer is right
  • 37. No your answer is wrong
  • 38. Yes your answer is right
  • 39. No your answer is wrong
  • 40. Yes your answer is right
  • 41. No your answer is wrong