Edit View History Bookmarks Window Help uic.blackboard.com ttps:/Juic.blackboard. Oes Not Open Automa. Pat Using rules of inenclot) There is an island that has two kinds of inhabitants: knights, who always tell the truth, and knaves, who always lie. You encounter two inhabitants of the island, A and B. A says: "At least one of us is a knave." What are A and B? Let p be the statement "A is a knighf and q be the statement "B is a knight. 1. (5 pt.) Assume that A is a knight. Use the rules of inference to determine whether B is a knight or a knave. (5 pt.) Assume that A is a knave. Use the rules of inference to show that this leads to a contradiction. 2. A prisoner must choose between two rooms, each of which contains either a lady or a tiger. There is a sign on the door of each room. Room I says: "a tiger is in this room or a lady is in the other room. Room I says "a lady is in the other room. Either both signs are true or both are false. Which room should the prisoner pick? Let p be the statement "roomI contains a lady and q be the statement "room II contains a lady. 3. (5 pt.) Assume that both signs are true. Use the rules of inference to determine which room contains a lady 4. (5 pt.) Assume that both signs are false. Use the rules of inference to show that this leads to a contradiction