X is a set and $\displaystyle \tau_c$ is a collection of all the subsets U of X such that X-U either is countable or X.

$\displaystyle X-\bigcup_{\alpha\in A}U_{\alpha}=\bigcap_{\alpha\in A}(X-U_{\alpha})$. (DeMorgan's Law--I understand this)

Now, it says the complement of $\displaystyle \bigcup_{\alpha\in A}U_{\alpha}$ is a subset of countable sets.

I don't get this. Can someone explain what is going on?

Thanks.