For each of the following, first write the argument in symbolic form, and then determine if it is valid or invalid. If the argument is valid, prove it using known logical equivalences and inference rules, and give a reason for each step. If it is invalid, demonstrate that by giving a counterexample and explain why your counterexample shows the argument is invalid. (a) If the team could not play good defence, or the forwards did not score enough goals, then the team would not have qualified for the playoffs and fans would have been disappointed. If the the team did not qualify for the playoffs, then tickets would need to be refunded. No tickets were refunded. Therefore, the team could play good defence. (b) I cycle to work or ride my motorcycle to work. If I cycle to work, then if I have an early class, I need to hurry. If don't complain, then I have an early class. Therefore, if I don't need to hurry then I don't complain.