01 03 are word problems given as a sequence of hypotheses/ premises ending with "Therefore conclusion". Show that each word problem is a valid argument Use rules of inference to show steps and reasons in the proof. 1) If I take a bus or subway then I'll be late for my appointment. If I take a taxi then I will be on time for my appointment and I will be broke. If I don't take the subway and don't take a bus then I will take a taxi. I will not be late for the appointment. Therefore, I will be broke. 2) If the interest rates decrease then the housing market will improve and utility prices increase Either the federal borrowing rate will decrease or construction will decrease. Interest rates decrease and utility prices increase. Either construction increases or the housing market does not improve. Therefore, the federal borrowing rate will decrease. 3) It is cold and not sunny today. We'll go for a run only if it is sunny. If we don't go for a run then it is not cold or we will go for a walk on the beach. We will watch a movie or we will not go for a walk on the beach. Therefore, we will watch a movie. For 04, 05 p,q, r,s, t,w are propositions, is the negation operator