Consider the following premises. Sarah is a sailor if and only if Joseph is sleeping. Mary is playing tennis if and only if it is raining. It is not raining. Sarah is not a sailor. Can we infer the following from them? Joseph is not sleeping.
 From the fact that Mary is playing tennis if and only if it is raining, and that it is not raining we can infer that Mary is not playing tennis. Finally, from the fact that Sarah is a sailor if and only if Joseph is sleeping, and that Sarah is not a sailor we can infer that Joseph is not sleeping. Therefore, the answer is yes.