# No nonfiction book published by Carriage Books has ever earned a profit. Since Carriage Books earned a profit on ever...

Minerva on September 14, 2019

C vs D

I was torn between C and D and ended up going with D. Can someone please explain this question? Thanks!

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Irina on September 14, 2019

@Minerva,

This is a tricky question! Let's look at the pattern of reasoning in the stimulus:

No nonfiction book (p) published by Carriage Books (q) has ever earned a profit (r).

p & q -> ~r

We can infer that if a book has earned a profit, it must be either fiction or published by another publisher:

r -> ~ p v ~q

Carriage books (q) earned a profit (r) on every book published last year

This statement tells us that r and p are true. We can tell from the above inference that if r is true

~ p v ~ q

must be true.

So either the book was fiction or it was another publisher. The statement tells us that Carriage books earned a profit, hence ~q is false, hence we can infer that ~ p must be true, as the argument correctly concludes:

Thus, it did not publish a nonfiction book last year.

~p

Let's look at (C):

PC (p) has never given a bonus (r) to an employee in its marketing division (q).

p & q -> ~r

We can infer that if an employee has received a bonus, either they must work for a different company or a different division.

r-> ~p v ~q

PC (p) gave bonuses (r) to every one of its system analysts last year.

This statement tells us that p and r are true.
We can tell from the above inference that if r is true

~ p v ~ q

must be true.

So either it was not PC or an employee worked for a different division. The statement tells us that PC gave bonuses, meaning ~p is false, hence we can infer that ~ q must be true, as the argument correctly concludes:

PC employed no system analysts in its marketing division.

~q

(C) is virtually identical to the argument in the stimulus.

Let's compare it to (D):

This argument is easier to understand if we rearrange the premises:

Waldsville only maintains business files (p) on individuals it does business with (q).

p -> q

~q -> ~p

JB has never done business (~q) with the city of Waldsville

~q

The city does not have a business file on JB.

~p

It is a valid argument, but the pattern of reasoning is entirely different. It simply concludes that because the precedent is true (~q), the antecedent must be true (~p), as opposed to the argument in the stimulus that concludes that one of the two options must be true, and since one is known to be false, the other must be true.

Let me know if this makes sense and if you have any further questions.

Minerva on September 16, 2019

This was a great explanation, thanks @Irina!

FS101 on July 7, 2020

The diagramming here is very confusing. I do not understand the symbols. I actually chose E because I thought that the stimulus was saying:

NF = not P (contrapositive: P = not NF)
P exists
NF does not exist

And E says:

CW = not IHF (contrapositive: IHF = not CW)
CW exists
IHF does not exist

I still do not understand why I am wrong. Thank you.

Veda-Bhadharla on August 11, 2020

I agree with Sheikh - I also think the diagramming here is incredibly confusing, and I also don't see how the question gives us multiple options as you say, so I am still confused as to why D is wrong.