Consider the following premises. For all z, z will write a letter if and only if z will drive a car. If Michael writes a letter, then Michael is driving a car. Can we infer the following from them? The fact that Michael drives a car does not imply that Michael is writing a letter.
 From the fact that for all z, z will write a letter if and only if z will drive a car we can infer that Michael is writing a letter if and only if Michael is driving a car. Finally, from the fact that Michael is writing a letter if and only if Michael is driving a car we can infer that if Michael drives a car, then Michael is writing a letter, which contradicts that The fact that Michael drives a car does not imply that Michael is writing a letter. Therefore, the answer is no.