Consider the following premises. If Linda goes running, then Karen is making tea. David is a nurse or Karen is not making tea. If David were a nurse, then Linda is running. Can we infer the following from them? David is a nurse if and only if Linda is running.
 From the fact that David is a nurse or Karen is not making tea we can infer that if Karen makes tea, then David is a nurse. From the fact that if Linda goes running, then Karen is making tea, and that if Karen makes tea, then David is a nurse we can infer that if Linda goes running, then David is a nurse. Finally, from the fact that if David were a nurse, then Linda is running, and that if Linda goes running, then David is a nurse we can infer that David is a nurse if and only if Linda is running. Therefore, the answer is yes.