Define the sets F1 and F2 recursively: Fi - 5 e F1 - ifn e F1, then 5n E F1 F2 - 5 e F2 - if n, m E Fi, then nm e F2 (a) Show that one of these definitions is technically ambiguous. (Remember that "ambiguous recursive definition" has a technical mathematical meaning which does not imply that the ambiguous definition is unclear.) (b) Briefly explain what advantage unambiguous recursive definitions have over ambiguous ones F2, is to show first that F C F2 and second that |(c) A way to prove that F1 F2 C F. One of these containments follows easily by structural induction. Which one? What would be the induction hypothesis? (You do not need to complete proof.) а