Please answer question 3,4 and part3(1a) with expalantion showing all the necessary steps. 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 l contains a lady" and q be the statement "room 11 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. Part Ill: Using rules of inference for quantified statements (50 pt.) Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid Let P(x) be "X is a student in this class," Q(x) be "X does not own a car," and R(x) be x takes the subway every morning," where the domain consists of all people. a. (15 pt.) Jack is a student in this class. Jack does not own a car. Everyone who does not 1. own a car takes the subway every morning. Therefore, someone in this class takes the subway every morning