Q7 - Failure to rotate crops

[deanmx]

How would you diagram the 1st and the 2nd sentence? For example the 2nd sentence has this format: "If...., .... unless ..." And if you could explain a little why choice C is correct. Thanks

[ManhattanPrepLSAT1]

Great that you're seeing the conditional relationships implied by 'if" and "unless." The statements in this stimulus are not easy to set up, especially when we have statements involving both "if" and "unless."

1. Failure to rotate crops depletes the soils nutrients gradually unless other preventative measures are taken. (Key: RC = rotate crops, DS = depleted soil, PM = preventative measures)

~RC + ~DS ---> PM

2. If the soils nutrients are completely depleted, additional crops cannot be grown unless fertilizer is applied to the soil. (Key: GC = grow crops, DS = depleted soil, F = fertilizer)

GC + DS ---> F

3rd and 4th sentences are proportional issues, which are very difficult to put into formal notation and probably not worth the effort.

We're given the additional piece of information that there were crops that were grown (vegetables) and that no fertilizer was used. This information feeds into the second statement very well.

The contrapositive of the second statement is

~F ---> ~GC or ~DS

We know that there was no fertilizer added so according to the constraint either no crops could be grown or the soil was not depleted. Since crops were grown (the vegetables) we can infer that soil had not been depleted. Answer choice (C) says that we know that the soil had not been depleted, but we are not sure of whether the crops had been rotated. This is true, the first statement does not apply, so we are not certain whether the crops had been rotated.

(A) is not true. It is not possible that the vegetables were grown in soil that had been completely depleted of nutrients.
(B) is too certain. We cannot establish on the basis of the evidence whether the crops had been rotated.
(D) is not necessarily true. It could be the case according to the stimulus that the health risks would be attributes of the use of pesticides. The argument allows for crops that are not fertilized to still be sprayed with pesticides.
(E) cannot be inferred. We cannot determine whether pesticides were sprayed on these vegetables.

I hope that helps you see this one a bit more clearly. This is definitely one of those borderline questions where it's not clear that putting the statements into conditional logic is much more valuable than just reasoning it through. In the end, i think it can't hurt to put it into notation for practice, so long as you're not under timed conditions!

[treebark_85]

Hi there, I have a question that kind of pertains to this question.
It is about combining conditional statements, I understand that the first statement is mapped out as ~RC + ~PM -> D

But, I am curious if this is because the statement is broken down into two components. We know that ~RC -> D, we also know that ~PM -> D. Therefore are we just combining these two statements? As in ~A-> B, ~C->B, Therefore ~A+~C-> B?

Thank You in advance.

[ManhattanPrepLSAT1]

Not exactly...

1. Failure to rotate crops depletes the soils nutrients gradually unless other preventative measures are taken. (Key: RC = rotate crops, DS = depleted soil, PM = preventative measures)

~RC + ~DS ---> PM

Follow the key word "unless" which introduces the necessary condition. In a very complicated form, we can see the statement in formal notation as the following.

~(~RC --> DS) ---> PM

My original version conveys the same information, but is much simpler to see. Notice that ~RC + ~DS denies the conditional statement ~RC ---> DS and so would imply ~(~RC ---> DS).

Honestly, this level of conditional logic is not being tested on the LSAT. Sure, it's there. But you don't need it.


More to your question though... If you combine

A ---> C
B ---> C

you would get

A or B ---> C

Thanks for the opportunity to dive into conditional logic. It's one of my favorite aspects of the LSAT!

[deanmx]

hmm I never knew that "If X then Y Unless Z" turns into "If X and ~Y then Z" Thanks!

[irini101]

Can I diagramed "~RC + ~DS ---> PM" as: ~RC --> ~DS --> PM

and "GC + DS ---> F" as: ~RC --> DS --> GC --> fertilizer --> pesticide?

I diagrammed this way during the prep test and I picked the correct answer but not sure whether my understanding is correct.

Thank you very much for help!

[ManhattanPrepLSAT1]

Can I diagramed "~RC + ~DS ---> PM" as: ~RC --> ~DS --> PM

and "GC + DS ---> F" as: ~RC --> DS --> GC --> fertilizer --> pesticide?

I'd be careful because in logic you can link together chains of reasoning such as:

A --> B
B --> C

Some people link this like

A --> B --> C

But that's not something I would ever do. The reason is that I want to know what the statements are actually saying, and I trust that I can link

A --> B
B --> C

together without writing them into one chain.

For the series
~RC --> ~DS --> PM

this says that if you don't rotate crops, then you won't have depleted soil, and this will imply that you have taken other preventative measures. But does it have to be true that if you don't rotate crops, that this will imply the other preventative measures? No. It could be the case that you simply have depleted soil.

So you could write the statement in several ways...

~RC + ~DS ---> PM

or you could express it this way...

~RC ---> (~DS ---> PM)

by putting the parentheses around the second conditional, we can see that that a failure to rotate crops doesn't imply that the soil is not depleted, but it does imply that if the soil is not depleted, then there must be other preventative measures being taken.

Does that answer your question?

[vincentsallan]

Hi, I found this question and explanation to be very confusing. The diagramming made no sense to me at all (don't understand why DS was diagrammed to be ~DS). Wouldn't that imply that the soil is not depleted? The diagramming just seems kind of different from the way I learned in my old TestMasters course and use of the LRB. The only way I can wrap my head around this problem is to think about it this way:

A failure to rotate the crops depletes the soil but not completely (at least not right away). You only need to use fertilizer if the soil has been completely depleted. You can still grow crops in soil that has been slightly depleted. It is for this reason why we don't know if the crops had been rotated. If the crops had been rotated, then of course we have no use for fertilizer. But also, the crops could have not been rotated and the soil could have only slightly depleted, this allowing for us to still grow crops without the need for fertilizer.

Does this make sense? Or am I thinking about it incorrectly?

[vincentsallan]

Also, how does the argument leave open for the possibility that pesticides could be used? It says "all other things being equal, if vegetables are grown in soil that has had fertilizer applied rather than being grown in non-fertilized soil, they are more vulnerable to pests and as a consequence must be treated with larger amounts of pesticides".

Does the part about "must be treated with larger amounts of pesticides" imply that it's possible for crops to be grown without fertilizer and still need pesticide since fertilizer makes you more susceptible but it's not the only time plants are susceptible to pests and thus need pesticide?

[ManhattanPrepLSAT1]

But also, the crops could have not been rotated and the soil could have only slightly depleted, this allowing for us to still grow crops without the need for fertilizer.

Your thought process is fine. According to the first statement in the stimulus, if one does not rotate crops, then the only way to have soil that is not depleted is to use other preventative measures. But we aren't given any information about whether other preventative measures were taken, so we cannot determine whether the vegetables had been grown in soil in which crops had been rotated.

According to the second statement, if no fertilizer had been applied then in order to grow vegetables, the soil cannot have been depleted.

Also, how does the argument leave open for the possibility that pesticides could be used?

According to the third statement, if fertilizer has been applied, the crops will need more pesticides, but the question stem makes clear that fertilizer had never been applied. So we cannot determine one way or another whether pesticides would be needed to a greater degree.

Does that answer your question?

[tzyc]

Hi,

I'm a little confused...How did you jump from ~(~RC→DS)→PM to ~RC→~DS→PM?
Same for GC+DS→F...
I thought it would be
~F→~GC+DS, so contrapositive GC+~DS→F...
What did I miss?

And...
~RC→~DS→PM and ~RC+~DS→PM means the same thing??
why those can be equal because to me they mean 2 diff. things, "IF-THEN" and "AND"?
A→B→C to A+B→C is fine, but reverse(A+B→C to A→B→C) is not Okey right??

Thanks.

[snoopy]

What is the strategy for stimuli with heavy conditional logic? As stated previously, this question is one of the "borderline" ones where reasoning through the argument is more valuable than diagramming the conditional logic. What is the appropriate strategy (the "Implemented Intention," if you will) for questions like these?

Thanks in advance!

[ohthatpatrick]

Conditional logic is ideally a tool we're using to ASSIST our understanding, not complicate it.

If we read an entire paragraph and think, "I think at least some of that chained together", then we should probably go back and seek to chain what ideas we can.

The sheer size of this paragraph makes it unlikely that you would ever be diagramming the whole thing (or that doing so would be prudent).

In order for things to chain, there have to be overlapping ideas.

Nothing in the 2nd sentence matches anything in the first sentence. The closest thing is "soil's nutrients are GRADUALLY depleted in the 1st" and "soil's nutrients are COMPLETELY depleted" in the 2nd, but those are not a match.

The 2nd and 3rd chain together, because they both deal with the idea of fertilizer having been applied. So I would pause there to synthesize the cause and effect. "If you run out of nutrients, you'll have to apply fertilizer, which means you'll have to use more pesticides."

My main takeaway from that cause/effect chain is, "run out of nutrients = bad".

The last sentence tells me what I already know: pesticides are bad.

So the 2nd / 3rd / 4th make it seem like "running out of nutrients leads to fertilizer which leads to pesticide which is crappy."

How would I prevent the soil from running out nutrients? I should either rotate crops or take "other preventive measures".

Because of the length of these sentences and the internal messiness of some of them, and because the question stem isn't a free-for-all Inference question (it's specifically "what do you know when there ISN'T fertilizer?") I wouldn't commit to diagramming anything.

But that means I'd spend that time otherwise taking a much slower 2nd read to try to process and understand the chain of ideas being presented.

When it comes to researching what happens when "fertilizer is never applied", I can see that
- from the rule in the 2nd sentence, there were still nutrients in the soil where these veggies grew.
(we probably rotated crops and/or took other preventive measures?)
- from the 3rd, all other things being equal, these veggies would have received less pesticide than veggies grown in fertilized soil

The implementation intention here seems unrealistically specific:
"IF I SEE a really long Inference paragraph with a funky question stem that specifically wants me to think about one thing, THEN I will probably try to understand the paragraph more like RC and think to myself "from the text, what can I infer about _______ ?"