Let f be a function from X into Y.

If is a family of subsets of Y, prove that = .

My thinking so far (which isn't a lot because I still don't have a grasp on this concept of indexed sets):

So how I'm understanding this is that the question is asking me to prove that the pre-image (and not the inverse function!) of the intersection of a certain family of subsets of Y (the set { }) is the intersection of the pre-images of .

The pre-image is in the domain. In this case the domain is X. So I have to show that the intersection of the pre-images of is the same as the pre-image of the intersection of all sets .

Is that even close?

Thanks for your time.