Q23 - A poor farmer was fond

[b91302310]

I know this is an assumption question and I have to close the gap between:
1) poor farmers -->honest, and
2) rich farmers--> dishonest

It's quite difficult for me even after I know the correct answer. The only reason I could guess for (A) to be correct is that the contrapositive of 2) is : honest-> poor farmer.

However, I cannot solve this question before I know the correct answer, so could anyone suggest how to attack this question at the first glance?

Many thanks.

[ManhattanPrepLSAT1]

This is one of my favorites.

R ---> ~P
~R ---> P
~H ---> D
H ---> ~D
=======
R ---> D

(Notation Key: R = rich, P = poor, H = honest, D = dishonest)

The subject is farmers, so I left them out of the notation. We should do that in the answer choices as well. And the there are two conditionals for each premise, since we know that you must be either rich or poor, and also honest or dishonest. Without both statements we couldn't capture that information.

We don't need all the premises in drawing the conclusion. From the first two, let's take R ---> ~P, since the R matches locations in the conclusion. From the second two premises let's grab ~H ---> D, since the D matches locations in the conclusion.

The reconstructed argument is

R ---> ~P

~H ---> D
=======
R ---> D

At this point the assumption should be clear, ~P ---> ~H. Take the contrapositive and the correct answer should say, "if you're honest, then you're poor." Best expressed in answer choice (A).

Not easy, but these sorts of questions can really allow you to stand out from everyone else if you can learn to manipulated conditional logic.

Does that clear this one up?

[geverett]

Matt,
I don't understand your explanation at all. haha. I just looked at this today and have a really firm grasp of conditional logic, but i can't seem to follow your train of thought up there to safe my life. Help me out if you can.

[ManhattanPrepLSAT1]

Let's take a closer look at how I arrived at some of the conditional relationships above.

We know that in this world you are either rich or poor. If you are rich, then you're not poor, but it's also saying that if you're not rich then you are poor. Those two statements together would imply that you one or the other: rich or else poor.

R --> ~P
~R --> P

We also know that you are either honest or dishonest. Again that's a one or the other scenario. If you are honest, then you are not dishonest, and if you are not honest, then you are dishonest. That would guarantee you are exactly one of else the other: honest or else dishonest.

H --> ~D
~H --> D

The conclusion reached is that if you are rich then you are dishonest.

R --> D

So that's where the conditional chains above came from. Using one of the premises from the first claim, one of the premises from the second claim, and the conclusion we can find the missing assumption.

R ---> ~P (selected because the sufficient condition matches the sufficient condition of the conclusion)
~P ---> ~H (here's the gap)
~H ---> D (selected because the necessary condition matches the necessary condition of the conclusion)
-----------
R ---> D

Does that make sense? There aren't trigger words in this one the same way there are in other questions testing conditional logic, but the meaning is implied. And there is a lab on advanced conditional statements available to students in the student center - check out the tab that says "Course Resources!"

[stm_512]

The most challenging part of this problem is that one of the seemingly relevant premises is completely irrelevant to solve this problem. The phrase "All poor farmers are honest" is written to confuse us, as we are generally inclined to focus on how to link a given premise to an answer choice in order to reach the author's conclusion in order to find the sufficient assumption.

Take the contrapositive of answer choice A), and it becomes, "if you are not poor, you are not honest". Since in the stimulus we are told that you are either poor or rich, and you are either honest or dishonest. We can translate the the contrapositive of A into, "if you are rich, you are dishonest", which is exactly the conclusion of the stimulus! Here we can see that the premise, "All poor farmers are honest" is completely irrelevant. It's actually the mistaken reversal of the stimulus' conclusion once you take its contrapositive.

That particular premise is simply a smokescreen to obscure test-takers into confusion, typical move by LSAT-makers.

[christine.defenbaugh]

We've done a cleanup round on this thread to consolidate a number of repeated questions into one (hopefully) clear reply! If you find that your question has not been fully answered, please post it here! (But please read this post carefully beforehand!)

1. But we didn't use the premise "All poor farmers are honest"!!

You're right, we didn't! We didn't need it, and frankly, it wasn't going to help. Annoying? Sure. But the LSAT has thrown extraneous conditionals into conditional-chain Sufficient Assumption questions before, and they surely will again!

How can you avoid getting tripped up by it? Focus on your task. Your job is to make the conclusion work, and you're only going to use the premises that help you get that job done. If a premise doesn't help you complete at least part of your task, then you should ignore it!

2. But the answer is just the contrapositive of the conclusion!

Sure is! If we found out that the contrapositive of the conclusion were true...well, since they are logically equivalent, that would absolutely prove the conclusion were true! Heck, if they straight up gave us the conclusion in an answer choice, that would prove the conclusion true also!!

Now, I don't generally expect to find a simple contrapositive of a conclusion as a Sufficient Assumption answer choice (much less the conclusion itself), because that's just way too simple! And honestly, this answer is a tad more complex than that. The real contrapositive of the conclusion would be:

All not-dishonest people are not-rich.

The only reason that we can read (A) as the same thing is because we are using the other premises to justify that 'not-dishonest = honest' and 'not-rich = poor'.

In other words, (A) is only the contrapositive of the conclusion if we use the premises to help us get there.

3. Why did Matt leave the 'farmer' out of his conditional notation?

That additional piece of information would have been extremely confusing to retain in the notation. Essentially, the conclusion is claiming there's a rule. But it's not a rule that applies to everyone -- just to farmers. Since our original premise-conditionals were all generic, it's easier to continue to work with the generic concepts, but just note to ourselves that the conclusion doesn't need to necessarily apply to everyone in the universe -- just farmers.

It would be like if I said "All red flowers are poisonous." If the rest of my information is all about color and toxicity, then maybe I want to think of that conclusion as something more like "(For flowers) If red --> poisonous".

There are at least 4 different ways to notate this kind of conditional statement, and some of them are extremely unweildy and confusing. Often times simply using part of the rule to indicate the category to which rule applies is the simplest construction.

4. Is there a way to do this without writing out a bazillionty conditionals and their contrapositives?

Sure, but it requires a conceptual comfort with the dichotomies presented in the first two premises: R v P, and H v D. Since these things are tied together in these pairs, connecting R to D similar to connecting P and D. We just need to figure out the right direction.

You won't be able to escape conditionals completely - after all, the conclusion IS a conditional. Contraposing the conclusion gives us: (for farmers) if not-dishonest --> not rich. Applying the dichotomies, that becomes (for farmers) if honest --> poor. Bingo!

5. Assessing the incorrect answers

On conditional Sufficient Assumption questions, predicting the correct answer is generally possible, and often ideal. However, these answers have some fun and funky characteristics that are worth noting:

(B) and (E): Both of these answers result in someone being a farmer. While my conclusion was a rule applied to farmers, I don't need to go deciding who is and isn't a farmer for that rule to work out.

(C): This is a flat out illegal reversal of the conclusion. This ain't helping us.

(D): This sounds an awful lot like that useless premise in the second sentence. In fact, it's identical to that useless premise, except that instead of just talking about farmers, it blows up to include everyone. But the limitation to farmers wasn't the problem with that premise, so blowing it up to 'everyone' doesn't help us a bit.

In fact, these other answer choices are so unhelpful in getting close to the conclusion that working from wrong-to-right is a completely worthwhile tactic here. If you were completely turned around on where to begin with sorting out the initial premise-dichotomies, kicking out some bizarre answer choices might have cleared your head!

[mornincounselor]

Conc: All R are ~H
-----------------------
Premise: P are H
Premise: Either P or R, either H or ~H

Right now, the conclusion is invalid because the problem allows the possbility that some R are still H.

If however we take choice (A) as true then we create a bicondtional:
P <---> H

Then the only way we are P is if we are H, and the only way we are H is if we are P. So therefore R<--->~H because that's the only possibility that the premises allow.

[uhdang]

There are two crucial points in this question.
First of all, like stm_512 and matt have mentioned, seemingly important premise is not used to reach the right answer choice. ("All poor farmers are honest." / P --> H)

Secondly, first two premises are bi-conditional relationship. So, our given premises and conclusion are,

Premise 1: R <--> ~P (Either Rich or Poor)
Premise 2: H <--> ~D (Either Honest or Dishonest)
Premise 3: P --> H (Poor are Honest; Not used though)
Conclusion: R --> D (Rich are dishonest)

The reason why they are bi-conditional and not conditional is that conditional relationship would allow either being both Rich/Honest and Poor/Dishonest (in case you write it as ~A --> B) or being neither Rich/Honest nor Poor/Dishonest (in case you write it as A --> ~B) as possibilities. For example, R --> ~P would allow that you are neither Rich nor Poor. But, you have to be at least ONE of them, according to the 'poor farmer'. And ~R --> P would allow you to be Both Rich AND Poor, although I doubt anyone wrote it as such.

Once we figured out all the premises and conclusion, we just need to find the right pieces and arrange them to see a 'missing link.'

Since Sufficient Condition of the conclusion is R, and necessary condition of it is D, we need to find R and D as sufficient condition and necessary condition from premises.

Premise 1(R <--> ~P) has R in a sufficient condition so let's take that. And we can have ~H <==> D from Premise 2 to get D in a necessary condition. This is where it might be confusing if you miss that premises are bi-conditional, because H --> ~D won't give you ~H --> D.

Looking at those premises and comparing them to reach the conclusion you can see that the red piece is what we need:

Premise 1: R <--> ~P
Assumption: ~P --> ~H
Premise 2: ~H <--> D
--------------------------
Conclusion: R --> D

And finally, a contrapositive of this assumption would be H --> P and it is A). Every honest farmer is Poor.

[melodyzhuangchina]

An easy and quick way to look at this:

Although the premise and conclusion give us the following:
Premise: rich —> ~poor
~rich —> poor
honest —> ~ dishonest
not honest —> dishonest
Conclusion: rich —> dishonest

We only need to look for the premises contain the element of the conclusion (rich and dishonest), and then find the missing conditional, which would be the correct answer!

So applying this:
the conclusion is: rich --> dishonest
we find the premises that contain these two element:
rich —> ~poor
not honest —> dishonest

therefore, we can find the missing conditional: ~ poor --> not honest.


Recap:
P: rich —> ~poor
not honest —> dishonest
C: rich —> dishonest
GAP: ~poor —> ~ honest, and the contrapositive: honest —> poor

[ghorizon09]

The answer is the contrapositive of the last sentence

All introduces a sufficient condition.

All Poor-------------> Honest
NOT Honest ------> Not Poor

All Rich ------------> Not Honest
All Honest --------> Not Rich


Answer A states:

Every honest farmer is poor = All honest ------> Not Rich

[a8l367]

Please review

All P are H
All H are P
=======>
Only P are H, Only H are P
=======>
All ~P are ~H, All ~H are ~P

(All ~P are ~H, All ~H are ~P) + (~P = R, ~H = D) = (R = D, D = R)

[YozzR849]

CONCLUSION:

Therefore, all rich farmers are dishonest.

REASONING:

In this world, you are either rich or poor, and you are either honest or dishonest.

All poor farmers are honest.

ANALYSIS:

I broke it down like this,

R or P
H or D

P(F) --> H

-------------
R(F) --> D

The contrapositive of P(F) H is D R(F).

So connect the chain with the conclusion.

R(F) --> D --> R(F)

Or

P(F) --> H --> P(F) This is the contrapositive of our chain. You’re either rich or poor and honest or dishonest.

So I’m looking for either

D --> R(F)

Or

H --> P(F)

Answer A: YES. H --> P(F). Just what we are looking for.

Answer B: NO. H (person) --> F. Out of scope. We’re not talking about honest people.

Answer C: NO. D (everyone) --> R(F). Out of scope. We’re not talking about everyone.

Answer D: NO. P (everyone) --> H. Out of scope. We’re not talking about everyone.

Answer E: NO. P (every person) --> F. Out of scope. We’re not talking about every person.