$(20$ pts$)$ Given the following logical reasoning, answer the following questions: I will buy a new car and a new house only if I get a job. I am not going to get a job. I will buy a new house.

:$.$ I will not buy a new car.

a$)$ Using the rules of inference approach, demonstrate the above argument's validity. Make sure to define proposition statements and additional variables to simplify the problem and be clear on each step taken.

a$)$

STUDENT:NAME:

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