Please provide each step using rules of inference. Do not give sentence explanation. Thanks!

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 Il 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 'room I contains a lady and q be the statement room II contains a lady. (5 pt.) Assume that both signs are true. Use the rules of inference to determine which room contains a lady. 3. 4. (5 pt.) Assume that both signs are false. Use the rules of inference to show that this leads to a contradiction