Let A, B, and C be disjoint denumerable sets. Show that A∪B∪C is also denumerable.

Given: A≈N, B≈N, and C≈N. Goal:A∪B∪C≈N

Suppose A,B, and C are non-empty disjoints sets such that A≈N, B≈N, and C≈N. Then, there exists functions f:A→N, g:B→N, and h:C→N that are one-to-one and onto N.

This is where my understanding kinda falls apart...Do have to set some knda of restriction? I can't find many examples in my book of this kind of stuff. Actaully, I'm probably just not making the connection.