I've been given a question on my problem set which I'm a bit stuck with. I'm getting the sense that the first part is easier than the second part, but I can't even seem to get the first part!

a) Let A, X, Y be sets such that . Show that . Therefore show that, for cardinals , if then .

b) Let A, B, X, Y be sets with and . Show that, apart from some exceptional cases, . What are the exceptional cases?

I'd really appreciate any help you can provide!