Consider the following premises. For all z, if z were a scientist, then z is a sailor. If David were a sailor, then Jessica is writing a letter. If Jessica writes a letter, then David is a musician. For all z, if z were a musician, then z is a scientist. Can we infer the following from them? David is a musician if and only if David is a sailor.
 From the fact that for all z, if z were a musician, then z is a scientist, and that for all z, if z were a scientist, then z is a sailor we can infer that for all z, if z were a musician, then z is a sailor. From the fact that for all z, if z were a musician, then z is a sailor we can infer that if David were a musician, then David is a sailor. From the fact that if David were a sailor, then Jessica is writing a letter, and that if Jessica writes a letter, then David is a musician we can infer that if David were a sailor, then David is a musician. Finally, from the fact that if David were a musician, then David is a sailor, and that if David were a sailor, then David is a musician we can infer that David is a musician if and only if David is a sailor. Therefore, the answer is yes.