I have having trouble with some simple problems involving the closure of sets. From my understanding the closure of a set is a set that contains all possible limits
a) $\{ (x,y) \in \mathbb{R^2} : xy< 1 \}$
b) $\{ (x,\sin(\frac{1}{x}): x > 0 \}$
c) $\{(x,y) \in \mathbb{Q^2}: x^2 + y^2 < 1 \}$
Here are is my attempt
a) $\{ (x,y) \in \mathbb{R^2} : xy \leq 1 \}$
b) Just itself? Not sure if this is even remotely meaningful
c) I think this is just the unit disk, not just why being members of only rationals makes any difference