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7. (10 pts.) Amelia visits several islands. The individuals oneach these islands are either truth-tellers or liars. Amelia isinterested in finding out whether everyone on a given island is atruth-teller, or whether everyone is liar, or whether there areboth truth-tellers and liars. (Note: it only takes one liar for anisland’s inhabitants to include both truth-tellers and liars.)Amelia is also interested in finding someone from whom to bum acigarette. (Yes, she shouldn’t smoke, but she does anyway andintends to stop soon.) In each of the following questions, usecomplete English sentences to present the reasoning that backs upyour answer. By the way, in this problem, and indeed every problem,you should remember that any universally generalized conditionalwhose antecedent-predicate is true of nothing is true. Amelia hasalready visited two of these islands. Now she visits two more.

a. On the third island, Amelia asks whether anyone on the islandsmokes. Everyone answers: “If I smoke, then everyone smokes.” Whatcan Amelia conclude about the third island? b. On the fourthisland, in response to the same question, everyone replies, “Someof us smoke, but I do not.” What can Amelia conclude about thefourth island?

b. On the fourth island, in response to the same question,everyone replies, “Some of us smoke, but I do not.” What can Ameliaconclude about the fourth island?