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

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Complete Question Explanation

Justify the Conclusion-SN. The correct answer choice is (A)

The farmer gives his children a few principles:

    Person → Rich or Poor

    Person → Honest or Dishonest

    Poor Farmers → Honest

He concludes:

    Rich Farmers → Dishonest

The farmer's premises do not warrant his conclusion. "Rich Farmer → Dishonest" is basically a Mistaken Negation of the idea "Poor Farmer → Honest." Since you are asked to justify the farmer's conclusion, you need to find a response that allows you to logically derive "Rich Farmers → Dishonest," and not need to make a Mistaken Negation.

Answer choice (A): This is the correct answer choice. "Honest Farmer → Poor" has the contrapositive "Rich → Honest Farmer." The contrapositive is best represented as "Rich → Farmer or Honest Farmer." With that fuller representation, you can see that a Rich Farmer would have to be a Dishonest Farmer, since it is not an option that a Rich Farmer is not a Farmer.

Answer choice (B): "Honest → Farmer." This idea makes "Farmer" a necessary condition for honesty, but does not show that Rich and Poor Farmers are different respective to Honesty, so this choice is wrong.

Answer choice (C): "Dishonest → Rich Farmer." You will not prove the conclusion by assuming the Mistaken Reversal of it.

Answer choice (D): "Poor → Honest." This choice yields the contrapositive "Dishonest→Rich," which is somewhat like a Mistaken Reversal of the desired conclusion.

Answer choice (E): "Poor → Farmer." This choice means that "Farmer" is a necessary condition for being poor, but does not show that there is a honesty difference between rich and poor farmers.
pele24
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Hi,
I have a question with regards to lesson 5, assum/justify/streng. review, Q 16 about poor farmers.

I prephrased it correctly, but if I did not prephrase the answer, I would solve it mechanistically and, as the result, choose an incorrect answer.
this is a justify question, and we can solve it mechanistically: new information in the conclusion will appear in the right answer choice. "Rich farmer" appears only in conclusion, and the only answer choice which contains it is C, but this answer choice is wrong.
Does it mean that we can't solve justify questions mechanistically all the time? or, it just me, may be i did not understand this method.

Thanks,

Lyuda
Steve Stein
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Hey Lyuda.

Good question! You are correct that the new information you mentioned—rich farmers—does appear in answer choice (C), but another answer choice says something about rich farmers as well, when you consider the conditional rules provided in the stimulus.

In this farmer’s absolute world, everyone is on one side of the fence or the other. If you’re not rich, you’re poor, and vice versa. If you’re not honest, you’re dishonest, and vice versa. According to these rules, rich farmers are implicitly referenced in correct answer choice (A) also: In a world where every single honest farmer is poor, none of those honest farmers are rich.

So this answer choice really says something about rich farmers as well: None of them are honest.

That one can be tricky, but let me know if it makes sense—thanks!
Steve Stein
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pele24
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yes, I got.
so, in contrapositive, not poor means rich. In this case, it makes sense.

Thank you!
RayMiller
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I looked for this question in the forum; however, I couldn't find it. If it was previously answered I apologize.

I got this answer wrong. After I got it wrong this is my analysis of why. Please provide guidance on whether my analysis is accurate and on anything I'm missing.

First I think this is a formal logic question.
The Diagrams:
    Either rich or poor: Not Rich--->Poor
    Either honest or dishonest: Not honest--->Honest
    All poor farmers are honest: PF--->H
    All rich farmers are dishonest: RF--->DH or Not PF--->Not H (I was torn about this)
In regards to inferences, can contrapositives be made for the all statements? I think so, but I'm not exactly positive. Is there a difference between contrapositives and reversibles?

Then the answer choices. The only way I understood 'A' to be correct is because all the other choices were too inclusive. Meaning instead of just making an assumption about 'farmers' in particular they in some way included 'every person.' In other words, the other answer choices' sufficient statement was every person or everyone. And the conclusion was not as inclusive of everyone. I have no idea if I'm totally off or not. Please Help.

Thanks
Nikki Siclunov
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This argument is indeed conditional in nature, and the reasoning can be diagrammed as follows:

Premise: PF :arrow: Honest

Conclusion: RF :arrow: Dishonest

Now, since you're always either rich or poor, and either honest or dishonest, the conclusion can be restated as follows:

Not PF :arrow: Not Honest

Answer choice (A) is the contrapositive of this statement, which - if true - would justify conclusion. None of the other answer choices do this:

(B) only proves that honest people are farmers, not that they are poor farmers
(C) is the contrapositive of the premise, which by itself does not justify the conclusion.
(D) is a broader restatement of the premise (applicable to everyone, even those who aren't farmers).
(E) does not specify whether the farmer in question is honest or not; even if it did, it would be a MR of the statement we are looking for.

Hope this helps!
Nikki Siclunov
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RayMiller
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I understand. Thanks Nikki
angie23
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For this problem, I understand that the premise: "All poor farmers are honest" (aka. pf :arrow: h) and the conclusion: "Therefore, all rich farmers are dishonest" (aka. ~pf :arrow: ~h) are mistaken negation of each other. However, how is A) the correct answer? I do not know how to arrive at the correct answer. I understand that A) is the contrapositive of the conclusion but when added to the premise it is just a mistaken reversal.
Nikki Siclunov
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Hi angle23,

Your understanding of the stimulus is correct. Since you are either rich or poor, and either honest or dishonest, the logical opposite of "poor" (i.e. "not poor") is logically equivalent to being "rich." The same applies to being honest and dishonest. Hence:

Premise: Poor :arrow: Honest

Conclusion: Poor :arrow: Honest

You are correct in your observation that the conclusion is a Mistaken Negation of the premise. It is incorrect to say, however, that answer choice (A) is a Mistaken Reversal of that premise. The Mistaken Reversal (or Negation) are errors in inference-making. In other words, they are fallacious only as deductions from the original condition. The conclusion is a Mistaken Negation, because conclusions are axiomatically inferred from the evidence presented. Answer choice (A), by contrast, is not an inference from any premise: it is merely a statement we are instructed to assume as true. So, if every honest farmer is indeed poor, we can diagram this as:

Answer choice (A): Honest :arrow: Poor

As you may notice, this is the contrapositive of the conclusion. The two are identical in meaning, which is why the conclusion is properly drawn if we assume that answer choice (A) is true. On a side note, when combined with the premise, answer choice (A) + Premise produce a bi-conditional statement in the following form:

Honest :dbl: Poor

Let me know if this helps!
Nikki Siclunov
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lenawilhide
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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?