Question

Let A = {1, 2, 3,.....,14}. Define a relation on a set A by

R = {(x, y) : 3x - y = 0, where $x,yϵA$}.

Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

Answer 1

We have,

3x - y = 0

$\Rightarrow 3x=y$ $\Rightarrow y=3x$

Putting x = 1, 2, 3, 4 we get, y = 3, 6, 9, 12 respectively

For x > 4, we get y > 14 which does not belong to set A.

$\therefore R=\left\{\right(1,3),(2,6),(3,9),(4,12\left)\right\}$

The arrow diagram representing R is as follow :

Clearly, Domain (R) = {1, 2, 3, 4},

Co-domain (R) = {1, 2, 3, 4....., 14} and Range (R) = {3, 6, 9, 12}