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IGCSE: SPM: Add Math: Function: 01-1 Relations
Contributed by: Chang
Additional Mathematics
IGCSE SPM
FUNCTION
RELATION
ALGEBRA
PART I
set X = { 1, 2, 3, 4 }
?
set X
1
2
3
4
This is a          of 4 elements.
The four elements are:
1, 2, 3 and 4
?
denoted by the set notation
set X
This is 
set Y
set Y = { 4, 5, 6, 7 }
set Y
4
5
6
7
The association of set X and set Y  are called
RELATION
?
set x = { 1, 2, 3, 4 }
set X
1
2
3
4
when they are connected by 
set x = { 4, 5, 6, 7 }
set Y
4
5
6
7
arrows
?
The association of set X and set Y  are called
RELATION
set x = { 1, 2, 3, 4 }
set X
1
2
3
4
when they are connected by arrows
set x = { 4, 5, 6, 7 }
set Y
4
5
6
7
We called this diagram 
set X
1
2
3
4
An arrow diagram
?
set Y
4
5
6
7
The                      between the 2 sets X and Y 
is the                         of the elements from      to 
relation
?
Mapping
?
 X
1
2
3
4
An arrow diagram
 Y
4
5
6
7
X
?
Y
?
We can use                                    to show   
of the set          and the set
an arrow diagram
X
?
 X
1
2
3
4
Y
?
 Y
4
5
6
7
relation
?
Relation of the sets can also be shown by
Ordered pairs
?
{              ,            ,             ,            }
( 1 , 4 )
?
( 2, 5 )
?
( 3, 6 )
?
set X = { 1, 2, 3, 4 }
set Y = { 4, 5, 6, 7 }
(x, y)
( 4, 7) 
?
Relation of the sets can also be shown by
A graph
?
set Y
5
?
4
6
?
1
2
?
3
?
set X
set X = { 1, 2, 3,}
set Y = { 4, 5, 6,}
Terms use in the 
RELATION
In set X, 
Domain
?
set X
a
b
c
d
= { a,b,c,d }
set Y
4
5
6
7
In set X, 
Domain
?
Objects
?
set X
a
b
c
d
= a,b,c 
= { a,b,c,d }
set Y
4
5
6
7
set X
a
b
c
d
Codomain
?
In set Y
set Y
4
5
6
7
= {4, 5, 6, 7 }
Range
?
=  4, 5, 6 
{           }
set X
a
b
c
d
Codomain
?
the difference
Images
?
In set Y
set Y
4
5
6
7
=   4, 5, 6, 7 
= 4, 5, 6
{                }
Domain
?
Objects
?
= q, r, s 
= { p, q, r, s }
set A
p
q
r
s
Range
?
Codomain
?
= {3, 5, 7}
Images
?
set B
2
3
5
7
 = {2, 3, 5, 7 }
= 3, 5, 7
Domain
Objects
= 1, 3, 4
?
= { 1, 2, 3, 4 }
?
 X
1
2
3
4
Range
Codomain
= {5, 6, 7}
?
Images
 Y
4
5
6
7
 = {4, 5, 6, 7 }
?
= 5, 6, 7
?
There are          types of 
1
2
3
1
2
3
4
?
1
2
3
1
2
3
relations
?
1
2
3
1
2
3
1
3
2
1
2
3
(b,   )
(c,   )
(d,   )
(a,   )
one to one
4
?
3
?
2
?
1
?
The relations between set R and Set S is
                     , (one object with one image)
R
b 
a
c 
d 
2
1
3
4
S
(a,   )
(a,   )
(d,   )
(a,   )
one to many
4
?
3
?
2
?
1
?
The relations between set R and Set S is
                     , (one object with many images)
R
b 
a
c 
d 
2
1
3
4
S
(  , 1  )
(d,   )
(  , 1  )
c
?
many to one
a
?
4
?
The relations between set R and Set S is
                     , (many objects with one image)
R
b 
a
c 
d 
2
1
3
4
S
many to many
(c,   )
(  ,   )
(d,   )
(  ,   )
c
?
a
?
3
?
The relations between set R and Set S is
                           , (one object with many images
              and many objects with one common 
                                      image
4
?
1
?
1
R
b 
a
c 
d 
2
1
3
4
S
every object has only one image
is a special relation
one to one
Relation
A function
It is a 
Is this a
function?
 yes
no
The relation between set R and set S is
R
b 
a
c 
d 
one to one
one to many
many to one
many to many
2
1
3
4
S
Is this a
function?
 yes
no
The relation between set R and set S is
R
b 
a
c 
d 
one to one
one to many
many to one
many to many
2
1
3
4
S
Is this a
function?
 yes
no
The relation between set R and set S is
R
b 
a
c 
d 
one to one
one to many
many to one
many to many
2
1
3
4
S
Is this a
function?
 yes
no
The relation between set R and set S is
R
b 
a
c 
d 
one to one
one to many
many to one
many to many
4
1
2
3
S
Is this a
function?
 yes
no
The relation between set R and set S is
R
b 
a
c 
d 
one to one
one to many
many to one
many to many
2
1
3
4
S
{(3,1),(2,4),(7,5)}
State the type of relation
one to one
one to many
many to one
many to many
{(1,2),(2,3),(3,4),(5,6)}
State the type of relation
one to one
one to many
many to one
many to many
{(2,4),(2,5),(3,4),(3,5)}
State the type of relation
one to one
one to many
many to one
many to many
{(1,3),(2,5),(1,4),(2,6)}
State the type of relation
one to one
one to many
many to one
many to many
{(1,2),(1,3),(3,3),(5,2)}
State the type of relation
one to one
one to many
many to one
many to many
Set B
4
2
8
6
The relation is
1
one to one
2
one to many
3
many to one
many to many
4
Set A
Set B
4
2
8
6
The relation is
1
one to one
2
one to many
3
many to one
many to many
4
Set A
Set B
4
2
8
6
The relation is
1
one to one
2
one to many
3
many to one
many to many
4
Set A
Set B
4
2
8
6
The relation is
1
one to one
2
one to many
3
many to one
many to many
4
Set A
Set B
4
2
8
6
The relation is
1
one to one
2
one to many
3
many to one
many to many
4
Set A
Additional Mathematics
IGCSE SPM
FUNCTION
RELATION
ALGEBRA
PART I
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