Consider the following premises. For all x_20, x_20 is a scientist or x_20 is not a doctor. For all x_20, x_20 is not a scientist. Joseph is driving a car if and only if Jennifer is a doctor. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not driving a car or William is a cashier.
 From the fact that for all x_20, x_20 is a scientist or x_20 is not a doctor we can infer that for all x_20, if x_20 were a doctor, then x_20 is a scientist via universal rewriting. From the fact that for all x_20, if x_20 were a doctor, then x_20 is a scientist, and that for all x_20, x_20 is not a scientist we can infer that for all x_20, x_20 is not a doctor via universal modus tollens. From the fact that for all x_20, x_20 is not a doctor we can infer that Jennifer is not a doctor via universal instantiation. From the fact that Joseph is driving a car if and only if Jennifer is a doctor, and that Jennifer is not a doctor we can infer that Joseph is not driving a car via biconditional elimination. Finally, from the fact that Joseph is not driving a car we can infer that Joseph is not driving a car or William is a cashier via addition. Therefore, the answer is yes.