Consider the following premises. If Thomas were a writer, then Michael is a nurse. If Michael were a nurse, then Robert is a lawyer. It is not late. It is late if and only if Robert is a lawyer. If Michael were a nurse, then Thomas is a writer. Can we infer the following from them? If we can, name the inference rule being used: Thomas is a writer.
 From the fact that it is late if and only if Robert is a lawyer, and that it is not late we can infer that Robert is not a lawyer via biconditional elimination. From the fact that if Michael were a nurse, then Robert is a lawyer, and that Robert is not a lawyer we can infer that Michael is not a nurse via modus tollens. From the fact that if Michael were a nurse, then Thomas is a writer, and that if Thomas were a writer, then Michael is a nurse we can infer that Michael is a nurse if and only if Thomas is a writer via biconditional introduction. Finally, from the fact that Michael is a nurse if and only if Thomas is a writer, and that Michael is not a nurse we can infer that Thomas is not a writer via biconditional elimination, which contradicts that Thomas is a writer. Therefore, the answer is no.