Let the set $ S = { A_{1}, A_{2}, A_{3},… } $ be a countably infinite set of statements. Let the set $V$ be defined as follows:

A) $S subset V$

b) For any $alpha in V,$ the negation of $alpha$ is also in V.

c) For any $alpha, beta in V$, $(alpha vee beta) in V$

d) $V$ does not contain anything else.

Determine whether $V$ is countable or uncountable (with proof).

Unfortunately I’m feeling kind of lost with this question and don’t really know where to start. My first thought was it may be countable since I was thinking of it as a union of countable sets, but I’m not sure if it is a countable union or not. Any guidance or a hint in the right direction would be much appreciated?