Question:
Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(x, y) : 3x − y = 0, where x, y ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.
Solution:
A = [1, 2, 3,..., 14]
R = {(x, y) : 3x − y = 0, where x, y ∈ A}
Or,
R = {(x, y) : 3x = y, where x, y ∈ A}
As
$3 \times 1=3$
$3 \times 2=6$
$3 \times 3=9$
$3 \times 4=12$
Or,
R = {(1, 3), (2, 6), (3, 9), (4, 12)}.png)
Domain (R) = {1, 2, 3, 4}
Range (R) = {3, 6, 9, 12}
Co-domain (R) = A