Determine whether the following arguments are valid or invalid. If it is valid, then you must state the rules of inference used to prove validity, but if it is not then you must provide an example to outline precisely why it is invalid. (n.b., You do not need quantified predicate logic expressions to complete this problem.) (12 marks

a. If you get regular maintenance on your car, it wont break down. If you care about your car, you make sure it gets regular maintenance. Rileys car broke down. Therefore, he did not care about his car.

b. If Jordan rides his bike in the winter, he ruins his bike. If Jordan ruins his bike and it is spring, he gets his bike fixed. It is spring but Jordan does not get his bike fixed. Therefore, Jordan did not ride his bike in the winter.

c. If my office floor is wet, or my office floor is dirty, it is because I wore my boots to school. I wore my boots to school if it is raining outside or if it is cold outside. It is not raining outside, but it is cold. Therefore, my office floor is wet.