Test Prep due October 3

Which topics and theorems do you think are the most important out of those we have studied?

I think the most important theorems are the ones that provide useful tools that allow us to look at a problem in a new way. That sounds very vague.

Here is an example: The idea that the contrapositive and the original statement have the same truth values. This allows us to approach the problem contrapositively, which can save time in situations where the direct proof would have gotten ugly. I think the theorems that allow us to look at proofs from a different approach are more useful than the smaller theorems one would use within a proof.

What kinds of questions do you expect to see on the exam?

Proofs. 😀 I think that it will be largely focused on proving various statements in a variety of ways, (types of problems similar to those on the homework). However, I hope they are less repetitive than the homework. Also, if we could avoid extremely weird proofs that require some sort of foreknowledge in order to solve or proofs that you have to "just see," that would be phenomenal.

What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.

I don't understand the solution to problem 4 on the practice exam. It seems as though the power set of {a,b,c} is {{empty set}{a}{b}{c}{a,b}{a,c}{b,c}{a,b,c}}. Thus A, or {a,b,c} is a subset of the power set of A. Or is {a,b,c} an element of the power set of A? If this is the case, why can it not also be a subset?

-Batman