The following problems require reasoning for their solution. To prove that an answer is correct requires an argument (often containing subsidiary arguments) whose premises are contained in the statement of the problem—and whose final conclusion is the answer to it. If the answer is correct, it is possible to construct a valid argument proving it. In working these problems, readers are urged to concern themselves not merely with discovering the answers but also with formulating arguments to prove that those answers are correct.

In the same mythical community described in Exercise 1, a stranger meets three other natives and asks them, “How many of you are politicians?” The first native replies, “We are all politicians.” The second native says, “No, just two of us are politicians.” The third native then says, “That isn’t true either.” Is the third native a politician?

Data From Exercise 1

In a certain mythical community, politicians never tell the truth, and nonpoliticians always tell the truth. A stranger meets three natives and asks the first of them,

“Are you a politician?” The first native answers the question. The second native then reports that the first native denied being a politician. The third native says that the first native is a politician. How many of these three natives are politicians?