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 busthen I will take a taxi. I will not be late for the appointment.Therefore, I will be broke.

2) If the interest rates drop then the housing market will improve.

Either the federal discount rate will drop or construction will decrease. Interest rates will drop and utility prices will go down. Either construction increases or the housing market does not improve.

Therefore, the federal discount rate will drop.

3) It is cold and not sunny today. We'll go for a run only if itis sunny. If we do not go for a run then 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.

Use rules of inference to show steps and reasons in the proof.