Proving a set is countably infinite $\left \{q \in \Bbb Q:q=\dfrac{a}{b}\ \text{where $a$ is even and $b$ is odd} \right \}$ Proving a set is countably infinite 
$$\left \{q \in \Bbb Q:q=\dfrac{a}{b}\  \text{where $a$ is even and $b$ is odd} \right \}$$
I am not sure how to go about solving this problem. I know it has something to do with Cantor Diagonalization, but I am not sure how to exclude the items that do not meet the criteria of the set. 

First the set is countable because is a subset of $\mathbb{Q}$. Now is infinite because the set $A=\{\frac{2n}{2n+1}:n\in\mathbb{N}\}$ is infinite. This follows from the fact that there is a bijection between $\mathbb{N}$ and $A$ ($\mathbb{N}$ is infinite). And from the fact that $A$ is a subset of your set.
