Set Concepts in Mathematics
Presented by
Ms. Bobade Swati Bhaskar
Department of Computer Sci. & IT
Deogiri College, Aurangabad
Maharashtra, 431 005
1
Set
Concepts
Set
Concepts
I
N
D
E
X
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
:
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
m
ore
numerous than
natural
numbers.
Defined cardinal
and
ordinal
no.
G
e
o
r
g
c
a
n
t
o
r
Venn
Diagrams
.a
.i
.
g
.
y
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
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
=
{M
o
nd
a
y
,
T
u
e
s
d
y
,
W
e
d
n
e
sd
a
y
,
T
h
u
r
s
d
ay,
Friday,Saturday}
•
Set k={a,e,i,o,u}Ru
le
me
t
ho
d
o
r
s
e
t
bu
i
l
d
e
r
method
•
All elements
of set
posses
a
common
property
•
e.g. set
of
natural
numbers is represented
by
e
.
g.
•
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 bloodtype}
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 bothSet
k and R are
equal.
•
We
can
write
as Set
K=Set
R
E
m
pty
se
t
s
•
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.
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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Presentation Transcript
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.
