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1. LANGUAGE OF
RELATIONS AND
FUNCTIONS
Mathematics in the Modern World
Group 4

2. Relations and Functions
“Relations and Functions” are the most important topics in
algebra. Relations and functions – these are the two different
words having different meanings mathematically. You might get
confused about their difference.
An ordered pair is represented as (INPUT, OUTPUT):
The relation shows the relationship between INPUT and
OUTPUT. Whereas, a function is a relation which derives one
OUTPUT for each given INPUT.

3. Relation
It is a subset of the Cartesian product. Or simply, a bunch
of points (ordered pairs). In other words, the relation between
the two sets is defined as the collection of the ordered pair, in
which the ordered pair is formed by the object from each set.
Example: {(-2, 1), (4, 3), (7, -3)}, usually written in set notation
form with curly brackets.
Domain (x) is the set of all first coordinates. (INPUT)
Range (y) is the set of all second coordinates. (OUTPUT)

4. Representations of Relation

5. Types of Relations

6. Function
A function is a relation which describes that there should be
only one output for each input (or) we can say that a special kind
of relation (a set of ordered pairs), which follows a rule i.e.,
every X-value should be associated with only one y-value is called
a function.
In other words, functions is a relation in which each input
(x) has only one output (y).
Note: All functions are relations, but not all relations are
functions.

7. Examples of Function

8. Examples of Function

9. Examples of Function

10. Try this: (a) List the domain and range of each relation.
(b) Determine if the relation is a function.
1. {(2,1), (-3,4), (0,5)}
2. {(1,3), (-2,4), (3,-2), (-2,7)}
3. {(1,4), (-2,0), (3,-6)}
4. {(-2,1), (0,5), (3,2), (0,-1)}
5. {(-1,-3), (1,3), (3,9)}

11. THANK YOU!!!

12. References:
[1] BYJU'S. (2024, February 18). Relations and Functions - Definition, Types,
and Examples. https://byjus.com/maths/relations-and-functions/
[2] Alvarado, Cristian & Cuevas, Mario Alberto. (2019). Multi-purpose
Cryptography Algorithm inspired by Cryptocurrency Techniques. 4.
[3] Math T. G. (2021, August 26). Relation and Function | What is the
difference between relation and Function | Types of Relation.
https://www.youtube.com/watch?v=mhrUi-
uVmLQ&t=497s&pp=ygUXcmVsYXRpb25zIGFuZCBmdW5jdGlvbnM%3D