Question

Let $A=\{1,2,3,....,14\}$. Define a relation $R$ from $A$ to $A$ by $R=\left\{\right(x,y):3x-y=0$ where $x,y\in A\}$. Write down its domain, co-domain and range.

Answer 1

The relation $R$ from $A$ to $A$ is given as

$R=\left\{\right(x,y):3x-y=0;x,y\in A\}$

i.e., $R=\left\{\right(x,y):3x=y;x,y\in A\}$

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

The domain of $R$ is the set of all first elements of the ordered pairs in the relation

$\therefore$ Domain of $R=\{1,2,3,4\}$

The whole set $A$ is the co-domain of the relation $R$

$\therefore$ Codomain of $R=A=\{1,2,3,.....,14\}$

The range of $R$ is the set of all second elements of the ordered pairs in the relation.

$\therefore$ Range of $R=\{3,6,9,12\}$