Consider the following premises. For all x, x is sad. For all x, x is not a writer. For all x, x is a writer or x is a police officer. For all x, if x were sad, then x is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which either x is a server or x is a police officer are not true.
 From the fact that for all x, if x were sad, then x is a server, and that for all x, x is sad we can infer that for all x, x is a server via universal modus ponens. From the fact that for all x, x is a writer or x is a police officer, and that for all x, x is not a writer we can infer that for all x, x is a police officer via universal disjunctive syllogism. Finally, from the fact that for all x, x is a server, and that for all x, x is a police officer we can infer that for all x, x is a server and x is a police officer via universal conjunction, which contradicts that There is at least one x for which either x is a server or x is a police officer are not true. Therefore, the answer is no.