Consider the following premises. Charles is a lawyer if and only if Jessica is writing a letter. Jessica is writing a letter or John is a doctor. Charles is a lawyer or John is not a doctor. Can we infer the following from them? Charles is a lawyer.
 From the fact that Charles is a lawyer or John is not a doctor we can infer that if John were a doctor, then Charles is a lawyer. From the fact that Charles is a lawyer if and only if Jessica is writing a letter we can infer that if Jessica writes a letter, then Charles is a lawyer. Finally, from the fact that if Jessica writes a letter, then Charles is a lawyer, that if John were a doctor, then Charles is a lawyer, and that Jessica is writing a letter or John is a doctor we can infer that Charles is a lawyer. Therefore, the answer is yes.