Is following Relation from $X$ to $Y$ is a Relation or not?

Question

$$X=\{1,2,3,4,5\} \text{ and } Y=\{1,3,5,7,9\}$$

$$R=\{(x,y)\mid y=2+x,x\in X, y\in Y\}$$

my textbook says it is a relation from $X$ to $Y$. But for $x=2$, $y=4$ but $4$ is not in $Y$. How is that possible?

Answer 1

Any relation between $X$ and $Y$ is a subset of $X\times Y$, so $R$ qualifies.

By the way, use $\in$ instead of $\epsilon$.