Contrapositive / Mistaken Reversal Chapter 2 Homework

[Tamra B]

On the Conditional Possibilities and Certainties Drill on page 2-59 I am missing the difference between creating the contrapositive and making a mistaken reversal.

For instance on question #4 - if (-N) = o, then what is the contrapositive?
Is it (-o)=N? From my review of the answer it seems this is a mistaken reversal.

So what is the contrapositive?

Thanks, Tamra

[Ron Gore]

Hey Tamra!

Glad to see you're plugging away at the homework!

Your representation of the conditional relationship threw me for a second. You wrote:

- if (-N) = o, then what is the contrapositive?
Is it (-o)=N?

While it is true that our system of representing conditional relationships using an arrow is merely a construct and not required to successfully diagram conditional reasoning, I recommend that you try use it since you'll be seeing it repeatedly in our materials. And, I understand that it may simply be you were uncertain of how to diagram the relationship in the context of this forum.

That nitpicking aside, let's look at the relationship:

N O

To show the contrapositive of this relationship, you have to do two steps: 1) reverse and 2) negate. So, the contrapositive is:

O N

It appears that you thought this might be the Mistaken Reversal. Remember that the Mistaken Reversal occurs when you do only one of the two steps required for the contrapositive, reversing the terms but not negating them. So, the Mistaken Reversal of the original relationship would be:

O N.

Hope this helps!

Thanks,

Ron

[Tamra B]

Thanks, that clears it up I will use the arrows next time too

[abares]

What should we do if we're not doing so well on the homework? On this section, the Logical Reasoning HW for L2, I got 19 out of 30 questions correct and many of them took me longer than the 1 min. 30 sec. that we should be allotted. I've been over concepts extensively and feel like I understand those and I went over the explanations wrong answers after. Is this cause for concern? If so, what can I do to start improving?

[Clay Cooper]

Hello abares,

Thanks for your questions. They are both good ones and very common.

First: Is this cause for concern? In a word: no. Obviously, your expectations will determine how acceptable 19 out of 30 is for you, but even if it is totally unacceptable, don't stress: I think you can count on that number improving if you continue to work hard. Specifically, the majority of the course material that remains, which you will soon be taught and on which you will drill extensively, depends heavily on the concept of conditional reasoning. You are going to see it over, and over, and over.... until you are sick of it. In the process, however, you will understand it far more thoroughly and you will get better at using it in all types of questions.

So, the answer to your first question brings me to the answer to your second: how can you improve? Simply put, by continuing to work hard in the course. If you keep doing your homework as thoroughly as you currently are, analyzing your results, and marking areas of concern for additional work, you will get the full benefit of everything your instructor has to teach you about conditional reasoning - and there is a lot. How it is related to and different from causal reasoning; how it makes Justify questions very formulaic; how tracking it can make assumption questions much easier; etc. Just keep your nose to the grindstone within the course, keep busting it, and you will improve, I am confident.

Thanks for your question. I hope this helps.

[abares]

Yes, thank you!