You are lounging on the beach on the island of liars and truth tellers with a large group of natives and you hear the following exchange: Alice: "We are all liars and Bob is a truth teller" Bob: "We are all liars or Carol is a liar What can you say about Alice, Bob and Carol? Justify your answer Hint: Let L(x) be the proposition that z is a liar; use quantifiers and De Morgan's laws for quantifiers in your answer. Consider the two cases where Alice is a truth teller or Alice is a liar