Consider the following premises. For all z_4, z_4 is a police officer if and only if z_4 will make tea. There is at least one z_4 for which z_4 will not drive a car. For all z_4, z_4 will make tea or z_4 will cook. For all z_4, z_4 is a police officer if and only if z_4 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all z_4, z_4 will not cook.
 From the fact that for all z_4, z_4 is a police officer if and only if z_4 will drive a car, and that there is at least one z_4 for which z_4 will not drive a car we can infer that there is at least one z_4 for which z_4 is not a police officer via existential biconditional elimination. From the fact that for all z_4, z_4 is a police officer if and only if z_4 will make tea, and that there is at least one z_4 for which z_4 is not a police officer we can infer that there is at least one z_4 for which z_4 will not make tea via existential biconditional elimination. Finally, from the fact that for all z_4, z_4 will make tea or z_4 will cook, and that there is at least one z_4 for which z_4 will not make tea we can infer that there is at least one z_4 for which z_4 will cook via existential disjunctive syllogism, which contradicts that For all z_4, z_4 will not cook. Therefore, the answer is no.