Conditional Reasoning Diagramming Drill #8

[Gy_lsat]

Hello, I have some questions.
First, 68page, #8. I think that contrapositive is NOT P5 -> NOT(P-R) . BUT. Solution is NOT P5 -> R-P. (WHY??!)
Likewise, #10,11,12 also I don't understand. Why is that?
Thank you for your help.

[Jon Denning]

Hey Gy - thanks for the question and welcome to the Forum! Let me see if I can help you out here

When we get sequences involving variables like P and R, as long as ties aren't allowed then it always MUST be one ahead of the other, either as P ahead of R, or R ahead of P. Thus, if we can determine that P is NOT ahead of R, then that means P must be AFTER R, so R is ahead of P. And of course vice versa.

In binary situations like this—where it's either scenario A or scenario B—as soon as you've ruled one out option you force the other to occur. So with contrapositives, saying NOT P R is the same thing as saying R P, because that's the only other option.

It'd be like saying either you or I must be first. And then we figure out that I'm third (so "not first"). What could we infer? You must be first! Saying "I'm not first" then is the exact same as saying "you are first," but since the second phrasing is an actual outcome rather than the more broad/uncertain prohibition, we always try to use the thing that WILL happen whenever possible.

I hope that helps!