Determining the cardinality of rational set

Question

I have two questions, but I don't even know where I can start to solve it, can you give me a hint?

The question is like (Forgive me if MathJax is going wrong):

Determine the cardinality of these sets

a) If X = $\{x \in \mathbb{R} | 1 \leqslant\ x \leqslant\ 3\}$

b) Be $\mathbb{Q}$ like $\mathbb{Q} = \{ p/q | p,q \in \mathbb{Z} q \gt 0\}$

Answer 1

For one you'll need to make use of the fact that $\omega$ (=$\mathbb{N}$) is bijectively equivalent to $\omega\times\omega$. A second useful fact is that every real number, except for countably many, has a unique binary expansion.

The last tool in you arsenal is the Cantor-Schröder-Bernstein theorem.