Consider the following premises. It is not raining. If John were a police officer, then it is raining. If John were not a police officer, then Karen is cooking. Can we infer the following from them? Karen is cooking.
 From the fact that if John were a police officer, then it is raining, and that it is not raining we can infer that John is not a police officer. Finally, from the fact that if John were not a police officer, then Karen is cooking, and that John is not a police officer we can infer that Karen is cooking. Therefore, the answer is yes.