Discrete Structures, using the following logical argument

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.

$--------------------$

Conclusion: 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.

b$)$ Combining the statement into the proposed tautology, use the laws of logical equivalence to demonstrate your findings above. Ensure clarity by introducing new variables in concise, single steps.