#23 - A poor farmer was fond of telling his children: "In

[Dave Killoran]

Hi Lena,

Good analysis overall! The problem with the argument in the stimulus is that it's missing a key piece, which is why the question stem for this one is a Justify the Conclusion. That's why it didn't make sense to you

The premises themselves look like this:

• You are either rich or poor:
  
  This is the diagram you supplied, which is R P. But, because rich and poor are two states that cannot concurrently exists, it's also R P. The operational result is the you can be one and only one of R or P.
  
  You are either honest or dishonest:
  
  Same as the first statement, although I tend to look at this as you are either H or H, but not both.
  
  All poor farmers are honest:
  
  This diagrams as P H. The contrapositive is H P. Of course, we can add the first premise to that, making the chain H P R

Ok, the contrapositive of that last statement is key to understanding how we get to the conclusion, which is R H. Why? Because you may note that the chain contrapositive is the Mistaken Reversal of what we need. And so we need an additional statement that will allow us to draw that conclusion.

Answer choice (A) serves that function. It is diagrammed as: H P. And, from the first premise we know that P R, so we have H P R. That's the same as H R, and the contrapositive of that is the conclusion in the argument.

A really tricky problem (and you can do it a bit faster by realizing that P = R and R = P, but that shortens it just a little bit; the explanation above uses the proper arrow relationships to show the links). Please let me know if that helps. Thanks!

[David Boyle]

My question: A poor farmer was fond of telling his children: "In this world, you are either rich or poor, and you are either honest or dishonest. All poor farmers are honest. Therefore, all rich farmers are dishonest."

I understand from some prelimary reserach that "all poor farmers are honest" is not relevant to find the answer.

But I think my confusion lies with how to diagram the premises. It is my understanding that OR statemetns are diagramed with a negative sufficient condition, like ~R -->P.

If this is correct, then ~R --> P; ~H --> D and the respective contrapositives are the premises. How does one get to the conclusion R--> ~H from just the premises?

Hello lenawilhide,

I think it is not just from the premise, but if you add in the answer, answer A, I think it was, "Every honest farmer is poor.": if you have that, h p, then slash p slash h. And if you're not p, you're r. And if you're not honest...you're dishonest! So, slash p slash h is the same as r d.

In that sense, "All poor farmers are honest" is not relevant. p h just doesn't help, really, since the contrapositive is slash h slash p, meaning if you are dishonest you are rich. But what if there are no dishonest people? Also, commonsensically, even if all poor farmers are honest, how does it preclude rich farmers from being honest too? So "All poor farmers are honest" isn't helpful (it looks like a mistaken reversal of answer A), but answer A is very helpful to get where we want.

Hope this helps,
David

[Jon Denning]

A questions was posed by a student today via email, and in an effort to provide maximum visibility I'm copying my reply here.

This is a really interesting Justify question, whether the correct answer must prove that the conclusion is true.

So let’s start with the conclusion we’re trying to prove and work from there! The farmer’s conclusion is that “all rich farmers are dishonest.” This is based on a few strongly-worded statements (with diagrams for reference):

1. People are either rich or poor. Not Rich --> Poor ; Not Poor --> Rich
2. People are either honest or dishonest. Not Honest --> Dishonest ; Not Dishonest --> Honest
3. All poor farmers are honest. Poor Farmer --> Honest ; Not Honest --> Not Poor Farmer

We need to figure out how to get from those premises to the conclusion.

The first two are important as they establish two dual options regarding poverty and honesty. That either/or situation means that when you show one is not the case (like not rich) then by default the other must be (poor).

Next, if we accept that all poor farmers are honest, then the contrapositive tells us that farmers who are not honest are not poor. And we know from statements 1 and 2 above that people who are not honest are dishonest (#2) and people who are not poor are rich (#1). Translated, then, the contrapositive of #3 is “All dishonest farmers are rich.”

You can probably see that that’s so close to our conclusion, but not quite what we need. In fact it’s a reversal! So we have to find an answer choice that would take us in the opposite direction, letting us go from rich to dishonest. If we knew Rich --> Dishonest, we would prove our conclusion!

There are two ways we could be told Rich --> Dishonest. One would be directly, a simple statement to that effect. But that doesn’t happen for us in the answers here. The other way is by the contrapositive. If we were given the contrapositive of Rich --> Dishonest, meaning Honest --> Poor, we’d have it! And sure enough that’s exactly what (A) tells us.

Knowing from (A) that every honest farmer is poor, and know from statements 1 and 2 that when we take the contrapositive not poor = rich and not honest = dishonest, we immediately arrive at our conclusion: every rich farmer is dishonest.

In fact, and finally, we could really prove this argument without even needing statement 3 above about poor farmers being honest; just know answer choice (A) that honest farmers are poor, and that negated poor becomes rich and honest becomes dishonest, we’d be able to show that all rich farmers are dishonest.

Note: I also have copied this response into our LSAT Forum as a new post at

I hope that helps clarify things! Thanks again!

[mpoulson]

Hello,

I don't understand how to tackle question 16. I recognize that "All farmers are honest" is a conditional statement and that conclusion "all rich farmers are dishonest" is also a conditional statement. However, I am not quite sure how to connect the two points for the conclusion to be properly drawn. This may in fact not be necessary, but it was my guess. Please explain for a simple man to understand. Thank you and appreciate all the help.

- Micah

[Robert Carroll]

Micah,

The stimulus tells us that all poor farmers are honest. Thus:

poor honest

The conclusion says:

poor honest

This doesn't work yet, so we need to fill in some information to make it work. Note that the contrapositive of the conclusion is:

honest poor

Note that I left out the fact that we're talking about farmers here. This is fine in the context, because these two statements are about farmers. If we talk about people more generally, we have to track that fact separately, but those two statements don't require that.

The contrapositive of the conclusion is what answer choice (A) states. That answer, combined with the premises, says, essentially, that the honest farmers and the poor farmers are the same set of people:

poor honest

Because rich farmers aren't poor farmers, they can't be honest either, so they are dishonest.

Robert Carroll

[mpoulson]

What confused me about answer A is the way it was written it doesn't seem to fit at as the contrapositive? I was expecting the contrapositive to read something more like if you are "honest (not dishonest) you are not a rich farmer". With A saying " every honest farmer is poor" it seemed to be changing the sufficient condition to include farmer. The necessary condition of the conclusion simply says "dishonest" not dishonest farmer. Can you provide more insight about this?

[Nikki Siclunov]

Hi mpoulson,

The entire argument is concerned exclusively with farmers. The first sentence ("you are either rich or poor, and you are either honest or dishonest") simply functions to clarify the logical oppositions at stake. Typically, the logical opposite of "poor" would be "not poor," whereas the logical opposite of "honest" would be "not honest." For simplicity's sake, here the logical and polar opposites coincide. Thus, the contrapositive of any conditional statement will be a positive statement:

Premise: Poor Honest
Concl.: Rich Dishonest

If answer choice (A) is true (Honest Poor), the addition of this premise to the original premise will immediately justify the conclusion. Answer choice (A) is, as already discussed, the contrapositive of the conclusion. The argument is concerned exclusively with the attributes pertaining to farmers. Sentence syntax makes it clear that "dishonest" is an adjective attributable to the farmers. The meaning of answer choice (A) would not be altered had it stated, "every honest farmer is a poor farmer."

Hope this helps!

[deck1134]

Hello,

I am really struggling on Justify questions. I can set them up correctly but still get the wrong answer. Here is what I did on this question:

Person ---> Honest or dishonest
Person ---> Poor Farmer or Rich Farmer
Poor Farmer ---> Honest

Conclusion: Rich Farmer ---> Not Honest

Prephrase: Some way to connect Rich Farmer with Not Honest. Since Poor-Farmer ----> Honest, by the contrapositive, NOT Honest ---> NOT Poor Farmer, which is equal to Dishonest---> Rich Farmer. Isn't that answer choice C?

Where am I going wrong? I am literally missing all of the justify questions and cannot seem to fix my problem with them despite a lot of practice.

I then looked for an answer choice that could allow

[Adam Tyson]

I think where you are going wrong here, deck, is that you are adding some detail to one of the farmer's claims that isn't there. The farmer never said that every person is either a rich farmer or a poor farmer - he said everyone is either rich or else poor. He allows for rich bakers, poor milkmen, rich teachers, poor bankers, etc. Nowhere does he say everyone must be a farmer!

As to answer D, the conclusion we are trying to prove is that all rich farmers are dishonest. Does "everyone who is dishonest is a rich farmer" prove that? No, that is a Mistaken Reversal of the conclusion. The premises here, together with that answer, would still allow for at least one honest, rich farmer. That claim would not conflict with the claim that everyone who is dishonest is a rich farmer or that every poor farmer is honest. Since we need to prove that a rich farmer must be dishonest, we need to know that every honest farmer is poor. Then there would be no way for there to be an honest, rich farmer, and the conclusion would follow logically.

[mo_wan]

I was able to eliminate B/D/E, but I am confused between A and C.

c) It Dishonest --> Rich Farmer wouldnt that imply that no Honest person is a Rich Farmer because we know that one can only be either or.

Could it still be true that Honest People are Rich Farmers? If so, why?

a) It says Honest Farmer --> Poor, so doesnt that just mean the no Dishonest person is poor?



Cheers