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

###### Question details

You are investigating a murder on the island of liars and truth tellers. You have assembled a group and you want to know 2 if the murderer is in that group. You know that the murderer is a liar. However, you don’t 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 x is a murderer in the group”. Let L(x) be the proposition “person x 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 x, let Say − Murderer(x) be a proposition that is true if x would say that there is a murderer in the group.