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Question: challenge you are investigating a murder on the island of...

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Challenge: You are investigating a murder on the island of liars and truth tellers. You have assembled a group and you want to know

if the murderer is in that group. You know that the murderer is a liar. However, you dont know which members of the group, if any are truth tellers. Moreover, you are only allowed to ask yes/no questions to the leader of the group and you want to minimize the number of questions you ask. Hint: Your questions may use propositional logic and quantifiers. Let M(x) be the proposition, person is a murderer in the group. Let L(x) be the person r is a liar Show how to determine if the murderer is in the group by asking two yes/no questions to the group leader . Show how to determine if the murderer is in the group by asking a single yes or no question to the leader. Hint: For a person r, let Say - Murderer(x) be a proposition that is true if x would say that there is a murderer in the group.

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