Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}.
Question:

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

Solution:

The relation R from A to A is given as

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

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

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

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 codomainof the relation R.

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

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

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