Question

The figure shows a relationship 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
$R$ is a relation from $P$ to $Q$
$P=\{5,6,7\}$
$Q=\{3,4,5\}$

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

$\left(ii\right)$ Roster form
$R=\left\{\right(5,3),(6,4),(7,5\left)\right\}$

Domain & Range
Domain is the set of first elements of ordered pairs in relation $R$
Hence, domain $=\{5,6,7\}$
Range is the set of second elements of ordered pairs in relation $R$.
Hence, range $=\{3,4,5\}$