Consider the following premises. For all y, y will cook if and only if y is a doctor. For all y, if y cooks, then y is a doctor. John is not a doctor. Can we infer the following from them? John is cooking.
 From the fact that for all y, y will cook if and only if y is a doctor we can infer that for all y, if y were a doctor, then y is cooking. From the fact that for all y, if y were a doctor, then y is cooking, and that for all y, if y cooks, then y is a doctor we can infer that for all y, y is a doctor if and only if y will cook. From the fact that for all y, y is a doctor if and only if y will cook we can infer that John is a doctor if and only if John is cooking. Finally, from the fact that John is a doctor if and only if John is cooking, and that John is not a doctor we can infer that John is not cooking, which contradicts that John is cooking. Therefore, the answer is no.