Question

The figure shows a relation between the sets $P$ and $Q$. Write this relation

$\left(i\right)$ In set builder form
$\left(ii\right)$ In roster form
What is its domain and range?

Answer 1

Given that
Set $P=\{9,4,25\}$ and set $Q=\{1,\pm 3,\pm 2,\pm 5\}$

Relation between $P$ and $Q$
The elements of $P$ are the square of elements of $Q$.
$\therefore x=y^2$

Set builder form
In set builder form, $R=\left\{\right(x,y):x=y^2,x\in P,y\in Q\}$

Given set $P=\{4,9,25\}$
set $Q=\{1,\pm 2,\pm 3,\pm 5\}$

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

Domain of $R=$ set of first elements of ordered pairs in relation $R=\{4,9,25\}$

Range of $R=$ set of second elements of ordered pairs in relation $R=\{-5,-3,-2,2,3,5\}$