Knights and Knaves Recall the Knights and Knaves puzzle we saw in class. In that fictional world there are two types of people. Knights - who always tell the truth, and Knaves - who always lie. It is impossible to distinguish them by appearance, but only by the truth of their statements. 1. One day a traveller was wandering around the island of Knights and Knaves, when he encountered two local inhabitants, P and Q. The traveller asked: "Is any of you a knave?" P replied: "At least one of us is a knave". Can you find out what P and Q are? If so, what are they? If not, explain why not, and what other information you would need to know. A replied: "If B is a knave, then I am a knave too". What are A and B? 2. Later on, the traveller met two other locals, A and B. He asked whether either of them is a knight Logical Identities Simplify the following propositions. Show all steps of your solutions