Consider the following premises. For all x_10, x_10 is a police officer or x_10 is happy. For all x_10, if x_10 were a police officer, then x_10 is a writer. There is at least one x_10 for which x_10 is not a musician. For all x_10, if x_10 were a writer, then x_10 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is not happy.
 From the fact that for all x_10, if x_10 were a writer, then x_10 is a musician, and that there is at least one x_10 for which x_10 is not a musician we can infer that there is at least one x_10 for which x_10 is not a writer via existential modus tollens. From the fact that for all x_10, if x_10 were a police officer, then x_10 is a writer, and that there is at least one x_10 for which x_10 is not a writer we can infer that there is at least one x_10 for which x_10 is not a police officer via existential modus tollens. Finally, from the fact that for all x_10, x_10 is a police officer or x_10 is happy, and that there is at least one x_10 for which x_10 is not a police officer we can infer that there is at least one x_10 for which x_10 is happy via existential disjunctive syllogism, which contradicts that For all x_10, x_10 is not happy. Therefore, the answer is no.