Consider the following premises. Michael is cooking if and only if Michael is fast. Jennifer is not playing tennis. If Michael cooks, then Jennifer is playing tennis. Can we infer the following from them? Michael is not fast.
 From the fact that if Michael cooks, then Jennifer is playing tennis, and that Jennifer is not playing tennis we can infer that Michael is not cooking. Finally, from the fact that Michael is cooking if and only if Michael is fast, and that Michael is not cooking we can infer that Michael is not fast. Therefore, the answer is yes.