Consider the following premises. It is raining if and only if William is rich. Karen is an electrician. If William were rich, then Karen is not an electrician. Can we infer the following from them? It is raining.
 From the fact that if William were rich, then Karen is not an electrician, and that Karen is an electrician we can infer that William is not rich. Finally, from the fact that it is raining if and only if William is rich, and that William is not rich we can infer that it is not raining, which contradicts that It is raining. Therefore, the answer is no.