Consider the following premises. Jennifer is cooking if and only if Barbara is poor. For all z, z is not poor. Can we infer the following from them? Jennifer is cooking.
 From the fact that for all z, z is not poor we can infer that Barbara is not poor. Finally, from the fact that Jennifer is cooking if and only if Barbara is poor, and that Barbara is not poor we can infer that Jennifer is not cooking, which contradicts that Jennifer is cooking. Therefore, the answer is no.