#19 - At a gathering at which bankers, athletes, and lawyers

[clarawater]

Hi, so I have been having a bit of trouble understanding this question from the December 2009 LR Section 2. I know that it is conditional reasoning, but I don't think I am diagramming it correctly. Any help would be appreciated!

December 2009, LR Section 2, Question Number 19

LSAT question removed by Admin.

The correct answer is E, but I had chosen C.

[Dave Killoran]

Hi Clarawater,

Thanks for the message. Because of copyright issues you can't actually post the text of the question (hence the board admin removed it), but just referring to it by test number, section number, and question number works equally well!

You question is a good one, and the stimulus would be diagrammed as:

A = Athletes
B = Bankers
L = Lawyers

L <--|--> B --> A

This is a classic conditional relationship, and there is only one inference that can be drawn here:

A some not L

Here's how it works: if you are going to make an inference, you would typically start at one of the "ends" of the chain. But, starting at L you can't "go anywhere" because you are faced with a double-not arrow immediately. So, we look to start at A. But, it looks like we may be stuck since there is an arrow coming from B to A (B --> A). However, we can "go backward" against that arrow, and what results is "some" (this is a concept discussed in the Logical Reasoning Bible, in the Formal Logic chapter, as well as in our Full-length and Virtual LSAT courses). So, we know that "A some B" exists. Then we can take the next step over to L, but we have to add a "not" in, resulting in A some not L. That is the exact wording of answer choice (C), and so (C) is correct (I think you may have looked at the answer key to section 3, because #19 in that section is E).

Questions like these seem very tricky at first, but if you get Formal Logic down, you can destroy a question like this in mere seconds. That's a huge advantage, especially as this question appears towards the end of the section.

If you have any quesitons, please let me know. Thanks!

[nsd1825]

I just want to confirm a diagram. MUST BE TRUE QUESTION

For the stimulus,
At a gathering at which bankers, athletes, and lawyers are present, all of the bankers are athletes and none of the lawyers are bankers.

Diagram

B-->A; B-->/L

Is this correct?

Credited Response, (C) Some of the athletes are not lawyers. (A-->/L)

[Jon Denning]

Those diagrams are correct. Combined you get A <-- B --> Not L, which gives you the A <-some-> Not L inference.

[nsd1825]

Jon,

Thanks for the note. I have to go back and freshen up on my formal logic work per Nikki.

My first post was beneficial.

Yours,


Nicholas

[beniakc]

#19
For the life of me I dont understand how C is the correct answer.
all bankers are athletes B-->A
None of the lawyers are bankers (L)-->B
Does that not translate to this:
(L)-->B-->A = no lawyers are athletes

[Steve Stein]

For quesion 19 on that one, the conditional statements break down as follows:

If you're a banker, you're an athlete:

B--> A

If you're a lawyer you're not a banker (and vice versa):

L --> NOT B
B --> NOT L

As we can see from above, if you're a banker, we know two things about you:
you're an athlete, and you're not a lawyer. We know that bankers are present, and every banker is an athletic non-lawyer.

Thus, we can safely conclude that at least one athlete is a non-lawyer, which is provided by correct answer choice C.

Let me know whether that clears this one up--thanks!

~Steve

[deborahjeng]

Why can't we conclude that at least one lawyer is not at athlete? I was stuck between answer B and answer C.

[Dave Killoran]

Hi Deborah,

You ask a good question, and one that can be very tricky in Formal Logic questions such as this one. Let's first combine the relationships discussed above into a single arrow diagram:

L B A


If you use our Formal Logic system, you know that you can't (or rather, shouldn't) start at L to make inferences. But you can start at A, and going "backwards" from A gives you "some," and then you can take the arrow over to L, and add a negative since it's a double-not arrow. That leads to this inference:

A some L

This reads out as "At least one athlete is not a lawyer," which is reflected in (C).

Answer choice (B) would diagram as:

L some A

Note the difference between this relationship and the one immediately prior--they are different (this one reads out as "At least one lawyer is not an athlete"). The problem here is, where does this diagram come from (or what would justify it)? We talk extensively about Formal Logic inferences in our books and courses, and a discussion of that is beyond the scope of what we can do here, but the gist is that there is no way to start from L and get to a relationship with A.

It's tricky, but this is also fundamental formal logic inferencing, and if you study how this works, the next time you see a question like this you can destroy it at light speed, and avoid the trap they place in answer choice (B)

Please let me know if that helps. Thanks!

[deborahjeng]

Dave,

Thank you for your response. It really helped. I just need to go over formal logic again. I read somewhere that is not included on the exam as often as it used to be. Is this true?