Consider the following premises. If Linda were not a doctor, then Robert is writing a letter. If Elisabeth drinks water, then Robert is writing a letter. If Linda were a doctor, then James is not a cashier. James is a cashier. Can we infer the following from them? Robert is not writing a letter.
 From the fact that if Linda were a doctor, then James is not a cashier, and that James is a cashier we can infer that Linda is not a doctor. From the fact that Linda is not a doctor we can infer that Linda is not a doctor or Elisabeth is drinking water. Finally, from the fact that if Linda were not a doctor, then Robert is writing a letter, that if Elisabeth drinks water, then Robert is writing a letter, and that Linda is not a doctor or Elisabeth is drinking water we can infer that Robert is writing a letter, which contradicts that Robert is not writing a letter. Therefore, the answer is no.