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

[collegen98]

Could someone please review my work on this one?

First sentence:
LoA or QJ --> OF

Second sentence:
~TFO --> Allow LoA
TFO --> ~Allow LoA

We have to prove the conclusion (third sentence): QJ --> TFO.

We end up with the chain QJ --> TFO --> ~Allow LoA.
the contrapositive is Allow Loa --> ~TFO --> ~QJ.

And we know from the first sentence that Ann has to either quit her job or take a leave of absence, so in the contrapositive we see that by allowing the leave of absence and her not quitting, we know that she will take the leave of absence because she has to do the other of the 2 options, which corresponds to answer choice (D).

I'm a little iffy about whether I explained that last part properly. Thank you!

[atierney]

Hello,

Yes! You explained it perfectly! We know that she must do one of the two options, and so when Tony finding out prevents one of the options, she must necessarily do the latter. Let me know if you have any questions on this.

[askuwheteau@protonmail.com]

Good afternoon,


This one was very challenging. Please examine my reasoning and let me know where my understanding could improve.

It appears that the entire conclusion of the stimulus consists of the following: QJ>OF

Premise one’s diagram: LA OR QJ>OF

Premise two’s diagram: Not TFO>ALA (The contrapositive being: Not ALA>TFO)

Conclusion’s diagram: QJ>TFO

To construct the logic chain: QJ>NOT ALA>TFO (requires that NOT ALA be inserted as it logically is an intermediary step as shown in premise two’s contrapositive)

My breakdown of the answer choices:

* A: The diagram here is TFO>IOH (with IOH having no match in the logic chain)
* B: Motivations for quitting her job are out of scope and irrelevant to the QJ>OF conclusion of the stimulus)
* C: The diagram here is WFC>LA (with WFC having no match in the logic chain)
* D: The diagram here is ALA>Not QJ (which is the exact contrapositive of the first portion of the logic chain)
* E: The diagram here is OF>QJ (with OF having no match in the logic chain)

Also, is the phrase “but not otherwise” abstractly equivalent in meaning to the “vice versa” double arrow indicator discussed in the LRB (2023 Ed., pg. 224)? I see this created a straight negation of premise two’s diagram as per Adam and Jon’s discussion on page 1 of the forum. Perhaps this unusual direction in the problem solving process is something not explicitly mentioned in the book, but possibly implied when “but not otherwise” is involved.

Thanks,

Jonathan Sloan

[askuwheteau@protonmail.com]

Although this is a Justify-type problem, we can understand the “Justify” portion as an assumption when analyzing the why and wherefore of the answer choices below.

Premise #1 diagram: TLA OR QJ>OTF (Take leave of absence or quit job, then offered fellowship)

Premise #2 diagram: FOTF (negated)>TLA (Technocomp doesn’t find out about fellowship offer, then leave of absence granted)

Conclusion: QJ>FOTF (if Anne will quits her job, then Technocomp found out about the fellowship offer)

Chain logic diagram combining common elements: FOTF (negated)>TLA OR QJ>FOTF>OTF

Legend:

* Out of Scope (OoS)
* NJ (Doesn’t Justify)

A: NJ (too restrictive as the argument never assumes that Technocomp can find out only by someone telling on Anne)

B: NJ (the motivations of Anne wanting the fellowship have no referent in the stimulus)

C: NJ (This statement has no assumptional basis in the stimulus and as such is OoS)

D: NJ [The sufficient condition “if Technocomp allows Anne a leave of absence” is equivalent to the sufficient condition of the diagram of premise #2 (i.e., Technocomp doesn’t find out about the fellowship offer). In other words, this answer choice is correct because it provides a repeat form of premise #2’s diagram (one of our four diagrams)]

E: NJ (too restrictive…the stimulus doesn’t provide any assumptional clues as to what is considered a necessary condition for the fellowship to be offered)

[Jeff Wren]

Hi Jonathan,

Overall, your reasoning looks good.

Here are a few comments.

First, the first sentence of the stimulus actually contains two conditional statements (and really three, as another is implied). The first half of the sentence states that Ann will take a leave of absence or will quit. That is an either/or conditional that can be diagrammed:

Not LA -> Q
and the contrapostive
Not Q -> LA

In other words, at least one of these two things will happen. However, because these two things are mutually exclusive (she can't quit and take a leave of absence), then exactly one of these must happen, which creates a second implied diagram

LA -> Not Q
and the contrapositive
Q -> Not LA

It is this second contrapositive that is actually used in the argument.

The second half of the sentence, regarding not doing either unless she's offered the fellowship, does not end up being used in the diagram for the argument.

The next premise does create a biconditional similar to "vice versa."

Not TFOTF <-> TALA
(Not TALA <-> TFOTF)

the second diagram (if Techocomp does not allow Ann to take a leave of absence, then Technocomp finds out) is the one that will be used.

Linking the relevant premises together, we get

Q -> Not LA (missing link) Not TALA <-> TFOTF

Basically we need to create the missing link in our chain

Not LA -> Not TALA

in order to complete the logical chain and justify our conclusion:

Q -> TFOTF

Answer D is the contrapositive of what we are looking for
TALA -> LA

Your analysis of the other answers looks good, but just be clear, you should be going into the answers with the prephrase that you're looking for:

Not LA -> Not TALA (or its contrapositive TALA -> LA)

I'm not exactly sure what you mean by:

"we can understand the “Justify” portion as an assumption when analyzing the why and wherefore of the answer choices below."

While there are times that assumptions are both sufficient and necessary to an argument (i.e. they overlap) often in conditional arguments like this one, you should approach each question type separately. For example, you shouldn't be using the Assumption Negation Technique on Justify questions.

[askuwheteau@protonmail.com]

You provided a unique perspective on a very challenging problem. Thank you Jeff!