broall
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.”
The farmer’s conclusion is properly drawn if the argument assumes that
(A) every honest farmer is poor
(B) every honest person is a farmer
(C) everyone who is dishonest is a rich farmer
(D) everyone who is poor is honest
(E) every poor person is a farmer
OFFICIAL EXPLANATION
(A) Yes. The passage defines categories: everyone is poor or rich, honest or dishonest, a farmer or a non-farmer. It then states that all poor farmers are honest; in other words, there are no dishonest poor farmers. It then concludes that all rich farmers are dishonest; in other words, there are no honest rich farmers. We can represent these statements as follows (where the crossed-out boxes indicate those combinations that do not exist):
From the table, we see that the passage assumes that every farmer who is honest is also poor.
(B) No. The passage defines categories: everyone is poor or rich, honest or dishonest, a farmer or a nonfarmer. It then states that all poor farmers are honest; in other words, there are no dishonest poor farmers. It then concludes that all rich farmers are dishonest; in other words, there are no honest rich farmers. We can represent these statements as follows (where the crossed-out boxes indicate those combinations that do not exist):
From the table, we see that the passage allows for honest people who are not farmers—namely, some poor and rich non-farmers).
(C) No. The passage defines categories: everyone is poor or rich, honest or dishonest, a farmer or a nonfarmer. It then states that all poor farmers are honest; in other words, there are no dishonest poor farmers. It then concludes that all rich farmers are dishonest; in other words, there are no honest rich farmers. We can represent these statements as follows (where the crossed-out boxes indicate those combinations that do not exist):
From the table, we see that the passage allows for dishonest people who are not rich farmers—namely, some poor and rich non-farmers).
(D) No. The passage defines categories: everyone is poor or rich, honest or dishonest, a farmer or a nonfarmer. It then states that all poor farmers are honest; in other words, there are no dishonest poor farmers. It then concludes that all rich farmers are dishonest; in other words, there are no honest rich farmers. We can represent these statements as follows (where the crossed-out boxes indicate those combinations that do not exist):
From the table, we see that the passage allows for people who are both poor and dishonest—namely, some non-farmers).
(E) No. The passage defines categories: everyone is poor or rich, honest or dishonest, a farmer or a nonfarmer. It then states that all poor farmers are honest; in other words, there are no dishonest poor farmers. It then concludes that all rich farmers are dishonest; in other words, there are no honest rich farmers. We can represent these statements as follows (where the crossed-out boxes indicate those combinations that do not exist):
From the table, we see that the passage allows for poor people who are not farmers.
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