EXPRESSING RELATIONS IN DIFFERENT FORMS

Let A and B be any two non-empty sets. A ‘relation’ R from A to B is a subset of Ax B ́ satisfying some specified conditions. If x ∈ A is related to y ∈ B through R , then
we write it as x Ry. x Ry if and only if (x, y)  R

Among several relations that exist between two non-empty sets, some special relations are important for further exploration. Such relations are called “Functions”.

The relations function may be represented by 

(a) a set of ordered pairs

(b)  a table form

(c)  an arrow diagram

(d)  a graphical form

Express the following relations as

i)  a table

ii) a graph

iii)  a mapping

Then, state the domain and range of the relation. 

Problem 1 :

{(-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3)}

Solution :

Given, {(-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3)}

Table :

x

-2

-1

1

2

4

y

1

0

2

-4

3

Graph :

graph1

Mapping a diagram :

expressingfuncindifferentform

Domain :

{-2, -1, 1, 2, 4}

Range :

{1, 0, 2, -4, 3}

Problem 2 :

{(-3, -3), (-1, 1), (0, 2), (2, -3), (2, 3)}

Solution :

Given, {(-3, -3), (-1, 1), (0, 2), (2, -3), (2, 3)}    

Table :

If x = -3 and y = -3

x = -1 and y = 1

x = 0 and y = 2

x = 2 and y = -3

x = 2 and y = 3

Graph :

graph2

Mapping a diagram :

expressrelationindifferentformq3

Domain :

{-3, -1, 0, 2}

Range :

{-3, 1, 2, 3}

This relation is not a function.

Problem 3 :

Express the relation

{(-1, -1), (1, 1), (2, 1), (3, 2)}

as

i)  a table

ii) a graph

iii)  a mapping

Then, state the domain and range of the relation. 

Solution :

Table :

If x = -1 and y = -1

x = 1 and y = 1

x = 2 and y = 1

x = 3 and y = 2

Graph :

graph31

Mapping a diagram :

expressrelationindifferentformq4

Domain :

(-1, 1, 2, 3)

Range :

(-1, 1, 2)

Problem 4 :

{(3, -2), (1, 0), (-2, 4), (3, 1)}

Solution :

Table :

If x = 3 and y = -2

x = 1 and y = 0

x = -2 and y = 4

x = 3 and y = 1

Graph :

graph4

Mapping a diagram :

Map41

Domain :

{3, 1, -2}

Range :

{-2, 0, 4, 1}

Problem 5 :

{(0, 4), (-4, -4), (-2, 3), (4, 0)}

Solution :

Table :

If x = 0 and y = 4

x = -4 and y = -4

x = -2 and y = 3

x = 4 and y = 0

Graph :

graph5

Mapping a diagram :

Map5

Domain :

{0, -4, -2, 4}

Range :

{-4, 0, 3, 4}

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