1a)
Shouldn't a) include "for any x,y"?
          c) " "  "   "   "    "   "
          d) 


2b) 
I don't think I like this question... I don't think it tests much. 

3) I think this question is very hard to parse. Honestly.

4) I like this one a lot

5) This one is also pretty good

6) Like this one too. 
a) should we be more clear about what "distinguishable" means?

7) Like this one

8) Like this one

9) Like this one

10) Like this one too

11) the solution is buggy, i think. you end
you proving that |vertices(B)| = |leaves(B)|
which isn't true.  the last two steps need to be changed. 

12) okay  

13) c) should we have a definition of "isomorphic"? I would think they
should know that, but I also though that they should recognize
"connected component".  

14) okay


In general, I think the test is very fair. Maybe kind of long, but
definitely looks reasonable in terms of the material covered. And the
level of difficulty also looks about right.  The problems that I said
I liked, I actually really liked (in terms of the material and the
level of difficulty).  Thanks for doing a good job at preparing the
final!

-Yana