I always thought an enclosure hadn't a roof and a cage would have a roof. Apparently this is not strictly so. Apart from that (I'm still not sure I want to accept it) I think it's a very clever quiz.
Thanks for the comment. Yes, an enclosure is simply something that closes something in - roof or no roof. It can be many things, including an area of field closed off by fences, a pig sty, a dog kennel, an envelope, and a bird cage (which typically doesn't have what I'd call a 'roof').