Consider the following premises. Mary is not a doctor. If Thomas were a writer, then Mary is a doctor. Sarah is poor if and only if Thomas is a writer. Can we infer the following from them? Sarah is not poor.
 From the fact that if Thomas were a writer, then Mary is a doctor, and that Mary is not a doctor we can infer that Thomas is not a writer. Finally, from the fact that Sarah is poor if and only if Thomas is a writer, and that Thomas is not a writer we can infer that Sarah is not poor. Therefore, the answer is yes.