Co-finite Topologies

Question

I would like someone to look through my solution to this problem and let me know if I have it correct or if I need to change anything. Any help would be greatly appreciated!

Answer 1

(b) If U,V are open disjoint sets, then exist
finite sets A,B with U = X - A, V = X - B.
Since (X - A) $\cap$ (X - B) is empty,
X = A $\cup$ B is finite, by DeMorgan's rules.