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