Let and be relations on sets and respectively.

The structure is:

1). extensional if ,

2).well-founded if

Show that if and are extensional and well-founded, then there is at most one isomorphism between them.

Hint: Consider for an automorphism of .

I have absolutely no idea how to do this question. I can't see how the hint is helpful. If I consider the automorphism, i'm not considering which I need to do.

Can anyone point me in the right direction?