Consider the following premises. For all x_11, x_11 is excited if and only if x_11 will make tea. For all x_11, x_11 will make tea or x_11 will write a letter. For all x_11, x_11 is not excited. For all x_11, x_11 is a musician or x_11 is rich. For all x_11, if x_11 were a musician, then x_11 is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is rich.
 From the fact that for all x_11, x_11 is excited if and only if x_11 will make tea, and that for all x_11, x_11 is not excited we can infer that for all x_11, x_11 will not make tea via universal biconditional elimination. From the fact that for all x_11, x_11 will make tea or x_11 will write a letter, and that for all x_11, x_11 will not make tea we can infer that for all x_11, x_11 will write a letter via universal disjunctive syllogism. From the fact that for all x_11, if x_11 were a musician, then x_11 is not writing a letter, and that for all x_11, x_11 will write a letter we can infer that for all x_11, x_11 is not a musician via universal modus tollens. Finally, from the fact that for all x_11, x_11 is a musician or x_11 is rich, and that for all x_11, x_11 is not a musician we can infer that for all x_11, x_11 is rich via universal disjunctive syllogism. Therefore, the answer is yes.