Final Exam


Link to the Final Exam

Truth Tables

A student wrote to ask about truth tables. I'm not by and large going to comment on what's correct or incorrect, but because I realize the notes weren't entirely clear on this particular point, I want to go ahead and clarify now.

You need to make sure your options cover each combination of possibilities for p, q, and r. So in the (relevant bits of the) truth table the student sent:

   p  q  r
   T  T  F
   T  F  T
   F  T  F
   F  F  T
   T  T  F
   T  F  T
   F  T  F
   F  F  T

...the given student was right to worry that the lower half is the same as the upper half. The 1st and 5th rows both cover the case where p is true, q is true, and r is false; you need to be sure that there's a row covering the case where p is true, q is true, and r is true.

If that wasn't clear, you can always take a look at the answer key to Homework 6, where there are a few tables illustrating the eight options for the truth/falsity of p, q, and r; you can model answers on those, if you need to.

Question 3.2

It's just been pointed out to me that question 3.2 isn't entirely clear. It asks for a true-or-false judgment on whether something is (a) one-to-one and (b) onto. That could mean either "true or false: it's both one-to-one and onto"; or "(a) true or false: it's one-to-one. (b) true or false: it's onto."

I intended the second. Answer 3.2a and 3.2b separately (for 2.5 points each).