#20 - Ann will either take a leave of absence from

[desmail]

Hi,

I can see how answer (D) is correct by process of elimination, but how does it GUARANTEE that the conclusion will follow?

If we take contrapositive of the conclusion:

She quits her job-->Techno found out

~Techno found out-->~She quits her job

We know that if Techno finds out, then she must take a leave of absence. Is (D) correct because we have to confirm she will accept the leave of absence for the conclusion to be solid? I just found this question really hard to solve; I feel like just because we know she will take the leave of absence this doesn't guarantee that the conclusion follows.

Thanks for any feedback!

[Adam Tyson]

Hey desmail. I agree with you that this is a confusing stimulus, so let's pick it apart and see what we know.

First, the opening sentence tells us that Ann will either take a leave of absence or she will quit her job. There's no alternative - she will do one or else the other. For that reason, when we diagram it, we can say that quitting her job (QJ) is the same as not taking a leave of absence, and taking a leave (LA) is the same as not quitting her job. It's a two-value system.

Next, we're told that shoe wouldn't do one of those unless she got offered the fellowship. We can set up the conditional statement there as something like "if LA or QJ -> OF". Put that together with the first sentence, and since we KNOW that she will do one of those things, then she MUST have been offered the fellowship. There's another known factor now.

Next, if Techno doesn't find out, they will allow the leave. If they find out, no leave. There are a couple of conditionals and contrapositives to deal with: if NOT TFO - > ALA; if NOT ALA - > TFO; if TFO -> NOT ALA; if ALA -> NOT TFO.

Finally, the conclusion: Ann quits only if Techno finds out, or "if QJ -> TFO."

How do we justify a conclusion like that? We need to link together two sufficient conditions (QJ and another one) that arrive at the same necessary condition - TFO. The other sufficient condition that gets us to TFO is "NOT ALA". We string them together this way: If QJ -> NOT ALA -> TFO (or, she quits her job ONLY IF she is not allowed to take a leave of absence, which happens ONLY IF Techno finds out about the fellowship). Answer choice D gives us the contrapositive of what we need: instead of "QJ -> NOT ALA" it gives us "ALA -> NOT QJ" (remember, in this two-value system, taking leave is equivalent to not quitting, and vice versa).

I hope that helped! It's a lot to deal with, I know.

Adam M. Tyson
PowerScore LSAT Instructor

[desmail]

Hey Adam,

Thanks for the great explanation! It really helped a lot. I just wanted to clear two things up:

1. How did you get two sets of contrapositives for the 2nd premise? (NOT find out-->ALA)?

2. For how you got to the conclusion, I understand how you found the missing piece to be QJ-->NOT ALA-->TFO.

But I initially diagrammed it as NOT ALA-->QJ-->TFO. Why would that be wrong? Is it because it doesn't really tell us how we got from QJ to TFO? When we are trying to justify a conclusion that already has "if" in it, are we trying to find a sufficient condition to tie us from the sufficient condition in the conclusion (QJ) to the necessary (TFO)? I think that's what you said earlier...

Thanks so much!

[Jon Denning]

Thanks for the questions. I'll just in here and see if I can help out:

1. The phrase "but not otherwise" at the end of prem2 is what causes the second conditional idea to be present. The first part of that sentence is "Not Find Out --> Allow Leave". "But not otherwise" tells us a second relationship is present: "Find Out --> Not Allow Leave" (which is essentially a straight negation of relationship 1). This is equivalent to a double arrow relationship, much like you'd get with a phrase like "if...but only if": "Not Find Out <---> Allow Leave" (and contrapositive "Find Out <---> Not Allow Leave"). Tricky idea, but hopefully that clears it up.

2. Are you saying that you diagrammed D as "Not Allow Leave --> Quit"? Because that's a mistaken negation of D, which actually says "Allow Leave --> Not Quit (Take Leave)".

It's from the contrapositive of that statement and it's connection to Technocomp finding out about the fellowship offer-- "Quit (Not Take Leave) --> Not Allow Leave --> Find Out Fellowship Offer" --that the conclusion is proven true. Think of it like this: how could we know Technocomp found out about the offer? If she's not allowed leave. So we need to show that quitting in the conclusion tells us that she wasn't allowed to take a leave of absence, and that's exactly what the contrapositive of D does: "Quit (Not Take Leave) --> Not Allow Leave". Trying to use the reversal of that won't work.

I hope that helps!

Jon

[desmail]

So in justify questions like this one, if we are given a conditional conclusion A-->C, we must justify how we got from A to C right? Which is why Adam was saying above that we need another sufficient condition?

What I did in my mistake was say (NOT B-->A-->C). But it still doesn't tell us how we got to the conclusion A-->C. I know that it is a mistaken negation, but I'm just asking if this train of thought can also be used to explain why NOT B-->A is wrong.

It also sounded right in my head (if not ALA-->quit job). We know that if she didn't get the leave of absence then she didnt go on leave of absence, which means she must have quit her job. But it seems that NOT ALA-->QJ-->TFO doesn't really answer the question because the gap between QJ and TFO is still left unexplained.

Thanks for your help!

[Jon Denning]

Yes, we need to prove the conclusion, so we must add information that makes the conclusion's conditional relationship true (shows A --> C, as you put it). And you're also correct in your analysis of why adding something that would lead to A is incorrect: it still doesn't connect A to C (A --> C) to prove the conclusion.

[ellenb]

Dear Powerscore,

I tried to diagram this question and the answer please let me know whether it is right.
i was not quite sure how they got the answer.
However, I tried.

the first sentence:

Take Leave of Absence or Quit Job--> Offered Teaching Position at Prestigious University

second sentence:

Not find out that she has been offered a fellowship-->will allow to take leave of absence

(but "not otherwise", not sure how to diagram that, I am taking a wild guess that it should be diagramed

Find out that offered fellowship--->will not allow to take leave of absence)

Last Sentence/Conclusion:

Quit Job--> Find out offered the Fellowship


Answer:

Allows to take the leave of absency--> Than will take leave of absency

How did they come up with this answer? Are my diagrams correct?

Thanks,

Ellen

[ellenb]

Did anyone see this question? Dear Powerscore team, please reply when you get a chance.

Thanks

[ellenb]

Mhh, I now have a different version of my diagram.
First of all, when we have:

either or it is diagrammed as:

A-->not B
B-->not A

cannot have both.

thus

for the first sentence: either leave of Absence or quit job (not both/ or either or)


Leave of Absence --> not quit job

quit job--> not leave of Absencce

(thus one or the other, cannot have both)

the last sentence before the conclusion says;
not find that have offered fellowship--> will allow to quit her job


the conclusion:

quit her job--> the univeristy found out that has been offered a fellowship

---------------

contrapositive of the last sentence before the coclusion

will not allow to take a leave of absence-->than university found about about the fellowship

if we combine it with one of the first statements than:


quit job --> will not allow leave of absence--> university found out about the fellowship.

Thus we just combined the statements.
Where we had A-->NOT B

and we had NOT B--> C from the contrapositve of the last statement before the conclusion.
So we got A-->NOT B-->C

RESULTING IN THE STATEMENET ABOVE (just retyped)
quit job --> not allow eave of abscency--> and university found out about the fellowship.
A not B C


and we just need A to get to C which i have here.
However, I am not sure why the answer is THIS WAY.

Why D is the correct answer, and how?

Thanks

Ellen

PS: now I have two versions, you can reply to either or both of them, I am not sure which one is right.

[Jason Schultz]

Hi ellenb,

I'm sorry about the delay, I was having technical issues.

I think you have overthought the problem somewhat. Let's think about this more relatable example for a second, before we dive into the logical diagramming.

Imagine you, Ellen, work at a law firm. You get offered the chance to live in Hawaii for a year and train dolphins (substitute awesome experience as needed). You don't want to lose your job (who would?), so you will ask for a leave of absence. But this offer is so good, that if they turn you down, you'll quit and do it anyway. However, the firm doesn't want Ellen, their best employee, to take a year off to train dolphins, so if they find out then they won't offer you leave.

That's Ann's situation.


Now lets look at the diagram. You correctly diagrammed the first sentence - the necessary condition is indicated by the "unless."

Leave of absence OR Quit ---> Offered fellowship.

You also correctly noted that the second sentence sets up two conditional statements:

Technocorp does not learn of fellowship ----> Technocorp offers leave of absence.
Technocorp does learn of fellowship ----> Technocorp does not offer leave of absence.

Notice that those two sufficient conditions are all-encompassing. Technocorp either learns about it or it doesn't. There is no third option. So one of those necessary conditions is guaranteed to occur.

The third and final sentence lays out the final relationship, with "only if" acting as a necessary condition.

Ann quits ---> Technocomp does learn of fellowship.

So youwind up with the conditional logic chain:

Ann quits --> Technocomp does learn of fellowship ---> Technocorp does not offer leave of absence.

But we know from the beginning that Ann will either quit or take a leave of absence, but we have no specific connection to anything that would cause Ann to take the leave. And thats what Answer D offers: A direct connection to the option of taking a leave of absence.

I think where you might be confused is that the logic chains are all in reverse chronological order, which is why it's important to keep Conditional Reasoning and Cause and Effect reasoning distinct.

Does that help?