[SOLVED] Finally in LaTex: Pre-images and indexed set.

Let f be a function from X into Y.

If http://qaboard.cramster.com/Answer-B...6150002563.gif is a family of subsets of Y, prove that http://qaboard.cramster.com/Answer-B...0837507949.gif = http://qaboard.cramster.com/Answer-B...8025004064.gif.

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 {$\displaystyle B_\alpha$}) is the intersection of the pre-images of $\displaystyle B_\alpha$ .

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 $\displaystyle B_\alpha$ is the same as the pre-image of the intersection of all sets $\displaystyle B_\alpha$.

Is that even close?

Thanks for your time.