let be the empty set. Let X be the real line, the entire plane, or, in the three dimensional case, all of three-space. For each subset of A of X, let

X - A be the set of all points x X such that x NOT A

(a) show that is both open and closed

(b) show the X is both open and closed (it can be shown that and X are the only subsets of X that are both open and closed)

(c) let U be a subset of X. Show that U is open iff X - U is closed

(d) Let F be a subset of X. Show that F is closed iff X - F is open.

I understand the concept of open and closed sets, but the thing is I don't understand what the question is describing to me before any of parts a,b,c or d in the first place. If I got a little bit on that I could actually understand how to solve the problem.