Solution: We need to show that \[ S = \left\{ C_r(x,y):x,y,r\in \mathbb{Q} \right\} \] is a countable set. Consider the map \[ \varphi : S \to \mathbb{Q} \times \mathbb{Q} \times \mathbb{Q} ,~C_r(x,y) \mapsto (r,x,y). \] It is clear that the map $\varphi $ is a bijection. Since $\mathbb{Q} $ is countable and countable product of countable sets is countable, thence $\mathbb{Q} \times \mathbb{Q} \times \mathbb{Q} $ is countable. Therefore, $S$ is countable.