Countability of $\mathbb Q\cap[0,1]$

Question

I do not understand why this set is countable $$\mathbb Q\cap[0,1]$$

Answer 1

It's well known that the intersection between a countable set and an uncountable set is countable. Intuitively, this makes sense because the intersection between two sets has size equal to at most the minimum size of the two sets that you are taking an intersection of. In other words, the size of $\mathbb{Q} \cap [0, 1]$ is at most the size of $\mathbb{Q}$, which is known to be countable.