Formal Logic Problem Set #2

[samhutch]

Hello,

My question is about Question2 in the Formal Logic Problem set in the most recent edition of the Logical Reasoning Bible.

Some of the world's most beautiful cars are Persian cats. However, it must be acknowledged that all Persian cats are pompous, and pompous cats are invariably irritating.

I can create the correct diagrams:
BC= Beautiful Cat
P=Persian
PO=Pompous
I=Irritating
BC P PO I
Inferences:
BC PO
BC I
P I

What I cannot understand is why choice C (Any cat that is not irritating is not a Persian cat) must be true-PLEASE HELP!

Answer key says it's because choice C is the contra positive of the 3rd inference, but I don't understand how that's possible.

[samhutch]

And nevermind! In case any one else has this issue--remember you can't make a contrapositive with a some or most statement, but all and none are just like conditional reasoning. If then

[Morgan O'Donnell]

Hi samhutch!

I just want to make sure you don't need this question answered. It looks like you figured it out already Let me know if you still need anything explained, and I will forward it along to our instructors!

Thanks for using the forum!

Morgan O'Donnell
PowerScore Test Prep

[kristinaroz93]

Hi, is e right for this reason:
persian cats--> irritating

so we can infer:

persian cats <-some--> irritating
which when reversed produces the idea that some irritating cats are persian cats, since the some arrow is reversible. But we cannot conclude from this whether some irritating cats are not persian cats as this idea is not discussed in the stimulus.


Please let me know if my reasoning here is correct, as I want to undertsand 100 percent why e is right=)

[Nikki Siclunov]

Hi Kristina,

You're absolutely correct. If all Persian cats are irritating, we can infer that some irritating cats are Persian. However, we cannot know whether some irritating cats are NOT Persian, because it is entirely possible (however unlikely) that all irritating cats are Persian.

Good job with the formal logic here

Nikki

[esther913]

Hi,

Is the term "beautiful cats" in (E) referring to the "world's most beautiful cats" in the stimulus?
I thought they were different terms and concluded that (E) was the answer.

Can I diagram (E) as I BC (for "Some irritating and beautiful cats") Not P ?

Any help would be greatly appreciated!
Thank you.

[Dave Killoran]

Hi Esther,

Thanks for the question!

The interesting thing here is they have covered themselves, because world's most beautiful cats would be a subset of beautiful cats. So, as soon as they start talking about world's most beautiful cats, you could automatically know it implies some beautiful cats in general. So, I don't think the difference you cite here drove their thinking (and instead it was the some are not portion), but it's also a test taking mistake because it's the only answer that drops the use of "world's." Your eye is kind of drawn to that usage, and they did it that way because of how the sentence is constructed.

Thanks, and good eye!

[esther913]

Wow
I never thought thatworld's most beautiful cats could be a subset of beautiful cats.
Now I properly understand why (E) cannot be the correct answer, thank you for the kind explanation