Consider the following premises. There is at least one z_3 for which z_3 is a scientist or z_3 will not cook. For all z_3, z_3 will cook if and only if z_3 is a scientist. Can we infer the following from them? For all z_3, if is not true that z_3 will cook if and only if z_3 is a scientist.
That contradicts the premises. Therefore the answer is no.