Consider the following premises. For all y, if y were a soldier, then y is writing a letter. For all y, if y writes a letter, then y is a soldier. Jennifer is not a soldier. Jennifer is writing a letter if and only if Patricia is driving a car. Can we infer the following from them? Patricia is driving a car.
 From the fact that for all y, if y were a soldier, then y is writing a letter, and that for all y, if y writes a letter, then y is a soldier we can infer that for all y, y is a soldier if and only if y will write a letter. From the fact that for all y, y is a soldier if and only if y will write a letter we can infer that Jennifer is a soldier if and only if Jennifer is writing a letter. From the fact that Jennifer is a soldier if and only if Jennifer is writing a letter, and that Jennifer is not a soldier we can infer that Jennifer is not writing a letter. Finally, from the fact that Jennifer is writing a letter if and only if Patricia is driving a car, and that Jennifer is not writing a letter we can infer that Patricia is not driving a car, which contradicts that Patricia is driving a car. Therefore, the answer is no.