Consider the following premises. Joseph is a musician or Karen is not a bartender. Charles is sleeping or Joseph is not a musician. If Charles sleeps, then Karen is a bartender. Can we infer the following from them? Charles is sleeping if and only if Joseph is a musician.
 From the fact that Joseph is a musician or Karen is not a bartender we can infer that if Karen were a bartender, then Joseph is a musician. From the fact that if Charles sleeps, then Karen is a bartender, and that if Karen were a bartender, then Joseph is a musician we can infer that if Charles sleeps, then Joseph is a musician. From the fact that Charles is sleeping or Joseph is not a musician we can infer that if Joseph were a musician, then Charles is sleeping. Finally, from the fact that if Charles sleeps, then Joseph is a musician, and that if Joseph were a musician, then Charles is sleeping we can infer that Charles is sleeping if and only if Joseph is a musician. Therefore, the answer is yes.