Consider the following premises. There is at least one x_8 for which if x_8 were sad, then x_8 is a scientist. For all x_8, x_8 will not drive a car. For all x_8, x_8 will drive a car if and only if x_8 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is not sad.
 From the fact that for all x_8, x_8 will drive a car if and only if x_8 is a scientist we can infer that for all x_8, if x_8 were a scientist, then x_8 is driving a car via universal biconditional elimination. From the fact that for all x_8, if x_8 were a scientist, then x_8 is driving a car, and that for all x_8, x_8 will not drive a car we can infer that for all x_8, x_8 is not a scientist via universal modus tollens. Finally, from the fact that there is at least one x_8 for which if x_8 were sad, then x_8 is a scientist, and that for all x_8, x_8 is not a scientist we can infer that there is at least one x_8 for which x_8 is not sad via existential modus tollens. Therefore, the answer is yes.