Set concepts

Set theory in Algebra Mathematics

1. Set ConceptsSet Concepts

2. Introduction

3. Shaan Education society’s
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 CHOUDHRY

5. SUBJECT: Mathematics
UNIT : Set concepts
STANDARD: IX

6. 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

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
xÎA i.e x belongs to set A.
4. If x is not an element of A we can write as
xÏA i.e x does not belong to A
e.g If Y is a set of days in a week then
Monday Î A
and January Ï 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 VennJohn Venn
.a .i
.g .y
.2 .2
.6 .8.6 .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
1.Empty set
2.Finite set
3.Infinite set
4.Equal set
5.Equivalent set
6.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 Æ 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= {§,¨,©,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 BÍA
•Every set is subset of itself i.e A
ÍA
• Empty set is a subset of
every set. i.e ÆÍA
.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 A B is represented by shaded
∩
part in venn diagram.
•Thus A B={x|x
∩
ÎA and xÎB}

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 of Set A= {1, 2, 3, 4, = {0, 2, 4,
6}
•5, 6} and Set B

29. Difference of two sets
1.The difference of set A- B is
set of all elements of “A”
which does not belong to “B”.
2.In set builder form
difference of set is:-
A-B= {x: xÎA xÏB}
B-A={x: x ÎB xÏA}
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
1.Definition of set andProperties of
sets
2.Set theory
3. Venn Diagram
4. Set Representation
5. 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
1.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