Write Relation as Ordered Pairs and Check Whether it is a Function
Question:
$$
\{(x,y): x+y=3,\ x,y\in\{0,1,2,3\}\}
$$
Solution
Given:
$$ x+y=3 $$
where
$$ x,y\in\{0,1,2,3\} $$
Taking values satisfying \(x+y=3\):
$$ 0+3=3 $$
$$ 1+2=3 $$
$$ 2+1=3 $$
$$ 3+0=3 $$
Therefore, the ordered pairs are:
$$ R=\{(0,3),(1,2),(2,1),(3,0)\} $$
Each element of the domain has exactly one image.
Therefore, the relation is a function.
$$ \boxed{\text{The relation is a function.}} $$