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