Cardinal of the set of all dense and enumerable subsets of $\mathbb R^2$ The problem statement:
Calculate the cardinal of the set consisting of all the dense and enumerable subsets of $\mathbb R^2$
The attempt at a solution:
I couldn't go farther than this: If $A$ is the set consisting of all the dense and enumerable subsets of $\mathbb R^2$, then $A\subset B \space$, $\space B=\{ S \subset \mathbb R^2: |S|=\aleph_0\}$. So $|A|\leq |B|={(c^2)}^{\aleph_0}=c^{2\aleph_0}=c^{\aleph_0}$
I have no idea what else to do, could anyone give me suggestions or hints on how could I go on?, for example, I could find a lower bound for the cardinal of $A$. Or maybe there is a bijective function from this set to another set $C$, where the cardinality of $C$ is easy to calculate.

You just need to go one step further:
$$|B|=\mathfrak{c}^{\aleph_0}=(2^{\aleph_0})^{\aleph_0}=2^{\aleph_0\cdot\aleph_0}=2^{\aleph_0}=\mathfrak{c}\;.$$
So $|A|\le\mathfrak{c}$, and you’ll be done if you can find $\mathfrak{c}$ different countable dense subsets of $\Bbb R$. What about sets of the form $\Bbb Q^2\cup\text{(something very simple)}\,$?
