Consider the following premises. For all z, z is sad if and only if z is a janitor. If Michael were a janitor, then Karen is not sleeping. Karen is sleeping. Can we infer the following from them? Michael is not sad.
 From the fact that for all z, z is sad if and only if z is a janitor we can infer that Michael is sad if and only if Michael is a janitor. From the fact that if Michael were a janitor, then Karen is not sleeping, and that Karen is sleeping we can infer that Michael is not a janitor. Finally, from the fact that Michael is sad if and only if Michael is a janitor, and that Michael is not a janitor we can infer that Michael is not sad. Therefore, the answer is yes.