Puzzle #184: More Alphabet Sets

Each letter of the alphabet has been put into one of three sets.

Set 1: A, F, H, K, M, N, P, R, T, V, W, X, Y
Set 2: B, D, E, I, L, Z
Set 3: C, G, J, O, Q, S, U

The solution has something to do with the shape of the letters. Depending on how you print it, Q might be considered to belong to set 1 instead. Depending on how you print them, I and some others might be considered to belong to set 1 or set 2, but commonly, I consider that they belong as above. If you get the basic rule, you will probably understand why.

What is the rule for which set a letter goes into? Tie-breaker question: What is that secondary rule about set 1 and 2?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, December 14, 2016 at noon Pacific Time. I will post the answer shortly after.