PPT: Relations and Functions

 Page 1


RELATIONS AND 
FUNCTIONS
Page 2


RELATIONS AND 
FUNCTIONS
Introduction
Finding Patterns
Mathematics helps us find 
recognizable links between 
changing quantities.
Daily Relations
We encounter many 
relations like brother-sister, 
teacher-student, or number 
m is less than number n.
Mathematical Precision
Functions capture 
mathematically precise 
correspondences between 
quantities.
Page 3


RELATIONS AND 
FUNCTIONS
Introduction
Finding Patterns
Mathematics helps us find 
recognizable links between 
changing quantities.
Daily Relations
We encounter many 
relations like brother-sister, 
teacher-student, or number 
m is less than number n.
Mathematical Precision
Functions capture 
mathematically precise 
correspondences between 
quantities.
Cartesian Products of Sets
Definition
A set of all possible ordered 
pairs formed from elements of 
two sets.
Example
A = {red, blue} and B = {b, c, s} 
forms six pairs: (red, b), (red, c), 
(red, s), (blue, b), (blue, c), (blue, 
s).
Ordered Pairs
Elements grouped in a specific 
order (p,q), where p * P and q 
* Q.
Page 4


RELATIONS AND 
FUNCTIONS
Introduction
Finding Patterns
Mathematics helps us find 
recognizable links between 
changing quantities.
Daily Relations
We encounter many 
relations like brother-sister, 
teacher-student, or number 
m is less than number n.
Mathematical Precision
Functions capture 
mathematically precise 
correspondences between 
quantities.
Cartesian Products of Sets
Definition
A set of all possible ordered 
pairs formed from elements of 
two sets.
Example
A = {red, blue} and B = {b, c, s} 
forms six pairs: (red, b), (red, c), 
(red, s), (blue, b), (blue, c), (blue, 
s).
Ordered Pairs
Elements grouped in a specific 
order (p,q), where p * P and q 
* Q.
Definition of Cartesian 
Product
1
Formal Definition
P × Q = {(p,q) : p * P , 
q * Q}
2
Empty Set 
Property
If either P or Q is 
empty, then P × Q 
will also be empty.
3
License Plate Example
A = {DL, MP , KA} and B = {01, 02, 03} creates nine 
possible codes.
Page 5


RELATIONS AND 
FUNCTIONS
Introduction
Finding Patterns
Mathematics helps us find 
recognizable links between 
changing quantities.
Daily Relations
We encounter many 
relations like brother-sister, 
teacher-student, or number 
m is less than number n.
Mathematical Precision
Functions capture 
mathematically precise 
correspondences between 
quantities.
Cartesian Products of Sets
Definition
A set of all possible ordered 
pairs formed from elements of 
two sets.
Example
A = {red, blue} and B = {b, c, s} 
forms six pairs: (red, b), (red, c), 
(red, s), (blue, b), (blue, c), (blue, 
s).
Ordered Pairs
Elements grouped in a specific 
order (p,q), where p * P and q 
* Q.
Definition of Cartesian 
Product
1
Formal Definition
P × Q = {(p,q) : p * P , 
q * Q}
2
Empty Set 
Property
If either P or Q is 
empty, then P × Q 
will also be empty.
3
License Plate Example
A = {DL, MP , KA} and B = {01, 02, 03} creates nine 
possible codes.
Visualizing the Cartesian Product
The order in pairs matters. For sets A = {a ¡, a ¢} and B = {b ¡, b ¢, b £, b ¤}, we get 8 distinct ordered pairs.
These pairs can represent positions in a plane if A and B are subsets of real numbers.