Consider the following premises. For all y_2, if y_2 were rich, then y_2 is cooking. James is rich or James is not cooking. Can we infer the following from them? If is not true that James is rich if and only if James is cooking.
 From the fact that for all y_2, if y_2 were rich, then y_2 is cooking we can infer that if James were rich, then James is cooking. From the fact that James is rich or James is not cooking we can infer that if James cooks, then James is rich. Finally, from the fact that if James were rich, then James is cooking, and that if James cooks, then James is rich we can infer that James is rich if and only if James is cooking, which contradicts that If is not true that James is rich if and only if James is cooking. Therefore, the answer is no.