Problem 5 on the exam is drawn from Chapter 2 and was therefore outside
of the specified syllabus. Technically, it can be solved using the tools
introduced in Chapter 1, but this is a hard question. What I had intended
was for this problem to be a standard proof from the syllabus. Please
consider your score on this exam as if it were out of 80, with a few of
you earning "bonus" points for partially solving a very hard question.