Consider the following premises. For all z, z will drive a car. It is raining if and only if William is climbing a mountain. William is not climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: It is not raining and Michael is driving a car.
 From the fact that it is raining if and only if William is climbing a mountain, and that William is not climbing a mountain we can infer that it is not raining via biconditional elimination. From the fact that for all z, z will drive a car we can infer that Michael is driving a car via universal instantiation. Finally, from the fact that it is not raining, and that Michael is driving a car we can infer that it is not raining and Michael is driving a car via conjunction. Therefore, the answer is yes.