Question

Form the Relation $R$ in the set $A=1,2,3,.13,14$ define as $R=(x,y):3x-y=0$

Answer 1

The relation $R\left(x,y\right):3x-y=0$ is defined on the set $A=1,2,3,\cdots ,13,14$.

This means the elements from the given set are to be chosen which satisfy $3x-y=0$.

Let $x=1$ and $y=2$, $x,y\in R$

Then,

$3\left(1\right)-2=1\ne 0$

So, the ordered pair $\left(1,2\right)$ will not satisfy the given relation.

Now, let $x=1$ and $y=3$, $x,y\in R$

Then,

$3\left(1\right)-3=3-3=0$

The pair$\left(1,3\right)$ satisfies the relation.

Continuing the same way, the relation will be,

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