Consider the following premises. Richard is cooking if and only if it is sunny. If Richard cooks, then Linda is a musician. If Linda were a musician, then it is sunny. Can we infer the following from them? Richard is cooking if and only if Linda is a musician.
 From the fact that Richard is cooking if and only if it is sunny we can infer that if it is sunny, then Richard is cooking. From the fact that if Linda were a musician, then it is sunny, and that if it is sunny, then Richard is cooking we can infer that if Linda were a musician, then Richard is cooking. Finally, from the fact that if Richard cooks, then Linda is a musician, and that if Linda were a musician, then Richard is cooking we can infer that Richard is cooking if and only if Linda is a musician. Therefore, the answer is yes.