How to calculate the cardinality of the complement of two countable sets of reals?

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Let $A,B\subseteq\Bbb R$ be countable sets. Denote by $A'$ and $B'$ the complements (in $\Bbb R$) of $A$ and $B$ respectively.

What is the cardinality of $C=A'\cap B'$?

I cant figure this one out, it seems that it depends on $A$ and $B$ because if their complement sets won't intersect then I've got empty set. Otherwise I should have countable set I guess.

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HINT: Use DeMorgan law to calculate $A'\cap B'$, and remember that the union of two countable sets is countable.