Consider the following premises. It is not sunny. Karen is a nurse or Thomas is not a poet. If Karen were a nurse, then it is sunny. If William were a lawyer, then Thomas is a poet. Can we infer the following from them? If we can, name the inference rule being used: William is not a lawyer.
 From the fact that Karen is a nurse or Thomas is not a poet we can infer that if Thomas were a poet, then Karen is a nurse via rewriting. From the fact that if Karen were a nurse, then it is sunny, and that it is not sunny we can infer that Karen is not a nurse via modus tollens. From the fact that if William were a lawyer, then Thomas is a poet, and that if Thomas were a poet, then Karen is a nurse we can infer that if William were a lawyer, then Karen is a nurse via transitivity. Finally, from the fact that if William were a lawyer, then Karen is a nurse, and that Karen is not a nurse we can infer that William is not a lawyer via modus tollens. Therefore, the answer is yes.