Consider the following premises. Joseph is working or John is not a musician. If Joseph works, then John is a musician. If John were a musician, then Joseph is working. Can we infer the following from them? If is not true that Joseph is working if and only if John is a musician.
 From the fact that Joseph is working or John is not a musician we can infer that if John were a musician, then Joseph is working. Finally, from the fact that if Joseph works, then John is a musician, and that if John were a musician, then Joseph is working we can infer that Joseph is working if and only if John is a musician, which contradicts that If is not true that Joseph is working if and only if John is a musician. Therefore, the answer is no.