I am studying for the Putnam competition in December and I want just a hint at how to do this problem, not a full solution please. I'm trying to develop a good methodology to approaching proofs.

A1. Determine, with proof, the number of ordered triples of sets which have the property that

(i) , and

(ii) . Express the answer in the form of , where a,b,c, and d are non-negative integers.

What's the best way to approach this?