Consider the following premises. Charles is not a police officer. If it is overcast, then Karen is a nurse. Charles is a police officer. Can we infer the following from them? Karen is a nurse.
 From the fact that Charles is a police officer we can infer that Charles is a police officer or it is overcast. From the fact that Charles is a police officer or it is overcast, and that Charles is not a police officer we can infer that it is overcast. Finally, from the fact that if it is overcast, then Karen is a nurse, and that it is overcast we can infer that Karen is a nurse. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.