Consider the following premises. If Michael were excited, then Jessica is a writer. If Jessica were a writer, then Michael is driving a car. For all x_10, if x_10 drives a car, then x_10 is excited. Can we infer the following from them? Jessica is a writer if and only if Michael is driving a car.
 From the fact that for all x_10, if x_10 drives a car, then x_10 is excited we can infer that if Michael drives a car, then Michael is excited. From the fact that if Michael drives a car, then Michael is excited, and that if Michael were excited, then Jessica is a writer we can infer that if Michael drives a car, then Jessica is a writer. Finally, from the fact that if Jessica were a writer, then Michael is driving a car, and that if Michael drives a car, then Jessica is a writer we can infer that Jessica is a writer if and only if Michael is driving a car. Therefore, the answer is yes.