Consider the following premises. It is not overcast. For all x_23, x_23 will drive a car if and only if x_23 is a scientist. It is overcast if and only if Barbara is driving a car. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not a scientist or Sarah is a police officer.
 From the fact that for all x_23, x_23 will drive a car if and only if x_23 is a scientist we can infer that for all x_23, if x_23 were a scientist, then x_23 is driving a car via universal biconditional elimination. From the fact that for all x_23, if x_23 were a scientist, then x_23 is driving a car we can infer that if Barbara were a scientist, then Barbara is driving a car via universal instantiation. From the fact that it is overcast if and only if Barbara is driving a car, and that it is not overcast we can infer that Barbara is not driving a car via biconditional elimination. From the fact that if Barbara were a scientist, then Barbara is driving a car, and that Barbara is not driving a car we can infer that Barbara is not a scientist via modus tollens. Finally, from the fact that Barbara is not a scientist we can infer that Barbara is not a scientist or Sarah is a police officer via addition. Therefore, the answer is yes.