Question

If A is a subset of the real line \(\mathbb{R}\) and A contains each rational number, which of the following must be true?

If A is open, then A = \(\mathbb{R}\)
If A is closed, then A = \(\mathbb{R}\)
If A is uncountable, then A = \(\mathbb{R}\)
If A is uncountable, then A is open.
If A is countable, then A is closed.