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 :
Mapping a diagram :
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 :
Mapping a diagram :
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 :
Mapping a diagram :
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 :
Mapping a diagram :
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 :
Mapping a diagram :
Domain :
{0, -4, -2, 4}
Range :
{-4, 0, 3, 4}
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