disconnection and component (topology problem)?

Question

Recall that a “disconnection” of X means a pair of nonempty separated sets A,B for which X = A \/ B.
Remember also that if C is a component of X, C is not necessarily “one piece in a disconnection of X.”
Prove that X has only finitely many components n(n>=2)
iff X has only finitely many disconnections.

any help please.
thank you.

Answer 1

I have this in a notebook somewhere...I will be back to update it