PT9.S2.Q23 - regarding the logic behind the question

TexAgAaron

Ok so this question gave me a world of trouble. I looked up the explanation given on Manhattan and I think I get it but I need confirmation.

My main problem is that the explanation given doesn't seem to use the contrapositive (which I attempted to use) but rather 2 separate worlds for each one.

"In this world, you are either rich or poor, and you are either honest or dishonest. All poor farmers are honest. Therefore, all rich farmers are dishonest."

Now taking away the farmers part, the explanation went on to list the premises as:
R-->/P If you are rich, then you are not poor
/R-->P If you are not rich, then you are poor.
H-->/D If you are honest, then you are not dishonest.
/H-->D If you are not honest, then you are dishonest.

These don't line up as contrapositives but rather separate worlds it seems. When used with the conclusion though, you can reach AC A as the right answer.

R-->/P
/P->/H
/H-->D

---

R-->D

So am I on the right track? You treat the premises as separate worlds?

thisissparta

Edit: Nvm, there was a loophole in my approach. Just as interested in explanations to this question!

jpandl

I am very new at the conditional logic and working through the translations to help me find answer choices, but if I may offer my two cents. I looked up the question and did it and I started by mapping out the translations and mine look like the ones you probably had as well but I was unable to make a connection between my translations and the right answer. I originally skipped right over A and was liking D, but than the fact that D was discussing "everyone who" rather than farmers seemed to go against the idea of a binary cut in the worlds of farmers. So than after going back up to A my eyes then recognized the thing that I thought was missing in D. Again sorry lack knowledge in the logic behind the question.