determine the cardinalities of the set

Question

So I am trying to figure out the cardinalities of the following sets (either finite, denumerable or uncountable ):

1. the set of all open intervals with rational midpoints
2. the set of all open intervals with rational endpoints

Any help or comments will be appreciated!!

Answer 1

HINT:

1. For every $r$ there is an interval of length $r$ around $0$.
2. Show that $\Bbb{Q\times Q}$ is countable.