- Introduction to Logic (4th ed.) by Irving M. Copi
(Highlight below for solution)
"In a certain mythical community, politicians always lie, and non-politicians always tell the truth."
First realize that all inhabitants must either be politicians or non-politicians; if a person is not a politician, how could he not be a non-politician? Therefore, we have a prescribed set of behavior for every inhabitant encountered.
“A stranger meets three natives, and asks the first if he is a politician. The first native answers the question.”
If one encounters a truth-saying non-politician, and asks if he is a politician, the answer will be “no.” If one encounters a lying politician, and asks the same question, the answer will be “no.”
Knowing that:
1) All natives must be of the set politicians, or the set non-politicians
2) Both sets would answer “no” when asked if they are politicians
We say that the first native answered “no” – though we do not know if he was telling the truth.
“The second native then reports that the first native denied being a politician.”
Because the first native said “no,” the second native is telling the truth, and therefore must be a non-politician.
“The third native says that the first native is a politician."
We do not know if the third is lying, but we do know that his statement conflicts with the first native’s denial of politicianhood. Either the first or the third is lying, but both cannot be lying, and both cannot be telling the truth.
“How many of these three natives are politicians.”
We know that:
1) One of the two, first and third, must be a politician
2) The second must be a non-politician.
Therefore, the answer is one.
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