I'd appreciate it if someone would look this over for me. This is probably easier than I am making it.

Let A, B, and C be subsets of a set X. I wish to show

First:

If then , but , thus

Thus . Since the roles of B and C are interchangable in the above by symmetry we also have that . Thus .

I can't figure out how to start the other half: . If I can't seem to go anywhere and if I get down to a statement that says , which seems to be a rather circular result. (I think this means since , but I'm a little sketchy on the logic here.)

Thanks in advance for the help.

-Dan