Question 1188254: Assume that teachers always tell the truth but that lawyers always lie. Wilson and Blair are either teachers or lawyers. Wilson says that Blair says that he (Blair) is a lawyer. Is Wilson a teacher or a lawyer?
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
(1) Assume that teachers always tell the truth but that lawyers always lie.
(2) Wilson and Blair  are either teachers or lawyers.
(3) Wilson says that Blair says that he (Blair) is a lawyer.
(4) Is Wilson a teacher or a lawyer?
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I re-wrote (edited) the problem in a way as I understand it and in a way
as it (in my understanding) should be sounded, pronounced and presented.
SOLUTION
Let assume that Wilson and Blair both are the teachers.
Then, according to the problem, they always tell the truth.
Hence, it is the truth what Wilson says, and, therefore, it is the truth that Blair is a lawyer.
It contradicts to the starting assumption that both are the teachers.
Hence, they both are the lawyers.
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| The last thing is to check that this conclusion |
| is consistent with the problem's formulation. |
+-----------------------------------------------------+
If they both are lawyers, then Wilson's statement is incorrect that Blair says he (Blair) is a lawyer.
Hence, Blair actually says that he is a teacher; but since Blair always says lie, he (Blair) is not a teacher;
hence, Blair is the lawyer, which is consistent with the problem.
ANSWER. Wilson and Blair both are the lawyers.
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Actually, the last check is checking if the problem is not self-contradictory . . .
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