Consider the following premises. For all z_1, if z_1 cooks, then z_1 is a politician. For all z_1, if z_1 were fast, then z_1 is not a politician. Linda is fast or it is cold. For all z_1, if z_1 were sad, then z_1 is a politician. For all z_1, z_1 is sad or z_1 will cook. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that for all z_1, if z_1 were sad, then z_1 is a politician, that for all z_1, if z_1 cooks, then z_1 is a politician, and that for all z_1, z_1 is sad or z_1 will cook we can infer that for all z_1, z_1 is a politician via universal disjunction elimination. From the fact that for all z_1, if z_1 were fast, then z_1 is not a politician, and that for all z_1, z_1 is a politician we can infer that for all z_1, z_1 is not fast via universal modus tollens. From the fact that for all z_1, z_1 is not fast we can infer that Linda is not fast via universal instantiation. Finally, from the fact that Linda is fast or it is cold, and that Linda is not fast we can infer that it is cold via disjunctive syllogism, which contradicts that It is not cold. Therefore, the answer is no.