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