GE6114
Math in the Modern World
Module 4- Mathematical Relations and Functions
Objectives:
1. Understand the mathematical language of relations and
functions.
2. Identify the relation as a function by applying the
properties.
The Language of Relations
and Functions
Relation
When two sets form a collection of ordered pairs
of (x,y) each of which coming from each set then it
is said that x R y.
x R y - binary relation R from set x to y
Relations
A relation in mathematics defines the relationship
between two different sets of information. If two sets
are considered, the relation between them will be
established if there is a connection between the
elements of two or more non-empty sets.
Example #1 (Relations)
In the morning assembly at schools, students are supposed to
stand in a queue in ascending order of the heights of all the
students. This defines an ordered relation between the
students and their heights.
Therefore, we can say, ‘A set of ordered pairs is defined as a
relation.’
Example #2 (Relation of sets)
This mapping depicts a relation from
set A into set B.
A relation from A to B is a subset of A
x B. The ordered pairs are
(1,c),(2,n),(5,a),(7,n).
For defining a relation, we use the
notation where, set {1, 2, 5, 7}
represents the domain. set {a, c, n}
represents the range.
Sets and Relations
Sets and relation are interconnected with each other. The
relation defines the relation between two given sets. If there
are two sets available, then to check if there is any connection
between the two sets, we use relations.
For example, an empty relation denotes none of the elements
in the two sets is same.
Relations in Mathematics
In Maths, the relation is the relationship between two or more
set of values.
Suppose, x and y are two sets of ordered pairs. And set x has
relation with set y, then the values of set x are called domain
whereas the values of set y are called range.
Example: For ordered pairs = {(1,2),(-3,4),(5,6),(-7,8),(9,2)}
The domain is = {-7,-3,1,5,9}
And range is = {2,4,6,8}
Functions
When two quantities x and y are related so that for
some range of values of x the value of y is determined
by that of x then we say that y is a function (f) of x.
A function relates an input to an output.
It is like a machine that has an input and an output
and the output is related somehow to the input.
Functions
Input, Relationship, Output
We will see many ways to think about functions, but
there are always three main parts:
The input
The relationship
The output
Example of a Function
Some Examples of Functions
x2 (squaring) is a function
x3+1 is also a function
Sine, Cosine and Tangent are functions used in
trigonometry
Equality of Functions
Two functions are said to be equal if and only they
have the same set of ordered pairs (x,y).
That Ends the MODULE 4!