Question

An arrow diagram shows a relation between the sets A and B.

Write the relation $R$ in roster form as well as in set-builder form.

• A. $R=\left\{\right(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5\left)\right\}$
  $\&R=\left\{\right(x,y):x=y^2,x\in A,y\in B\}$
• B. $R=\left\{\right(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5\left)\right\}$
  $\&R=\left\{\right(x,y):x=\sqrt{y},x\in A,y\in B\}$
• C. None of the above
• D. $R=\left\{\right(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5\left)\right\}$
  $\&R=\left\{\right(x,y):y=x^2,x\in A,y\in B\}$
  

Answer 1

The correct option is A $R=\left\{\right(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5\left)\right\}$

$\&R=\left\{\right(x,y):x=y^2,x\in A,y\in B\}$
As we can easily see, the roster form of the relation is,

$R=\left\{\right(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5\left)\right\}$

Now, for the set-builder form, we will have to find a condition or property by which the elements in A are related to the elements in B.

We can observe from the roster form that the first element of each ordered pair is the square of the second element.
i.e, the relation contains the elements $(x,y)$ where, $x=y^2$

So, the set-builder form of the relation R is,

$R=\left\{\right(x,y):x=y^2,x\in A,y\in B\}$