Hey, I am really stuck on a question so if anyone can help me I would be very grateful.

Show that the set of finite unions of closed intervals $\displaystyle \{ \cup^n_{i=1} [x_i,y_i] :$ $\displaystyle 0 \le x_i \le y_i \le 1$ $\displaystyle n \in \mathbb{N} \}$ in $\displaystyle X = [0,1]$ has the f.i.p.

I know that for a collection of sets to have the finite intersection property means that each nonempty finite subcollection of these sets has a nonempty intersection.

But I am unsure how to do this question and how to set it out.

Thanks in advance for any help.