Consider the following premises. Susan is cooking if and only if it is overcast. If it is overcast, then Barbara is playing tennis. For all z, z will not play tennis. Can we infer the following from them? Susan is cooking.
 From the fact that for all z, z will not play tennis we can infer that Barbara is not playing tennis. From the fact that if it is overcast, then Barbara is playing tennis, and that Barbara is not playing tennis we can infer that it is not overcast. Finally, from the fact that Susan is cooking if and only if it is overcast, and that it is not overcast we can infer that Susan is not cooking, which contradicts that Susan is cooking. Therefore, the answer is no.