Consider the following premises. For all z, z will cook. For all z, z will work. For all z, z is happy or z will not work. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is happy and z will cook.
 From the fact that for all z, z is happy or z will not work we can infer that for all z, if z works, then z is happy via universal rewriting. From the fact that for all z, if z works, then z is happy, and that for all z, z will work we can infer that for all z, z is happy via universal modus ponens. Finally, from the fact that for all z, z is happy, and that for all z, z will cook we can infer that for all z, z is happy and z will cook via universal conjunction. Therefore, the answer is yes.