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