Consider the following premises. For all x_14, if x_14 were a writer, then x_14 is a politician. For all x_14, if x_14 were a politician, then x_14 is a writer. For all x_14, x_14 is not a writer. There is at least one x_14 for which x_14 is a politician or x_14 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, neither x_14 will write a letter nor x_14 will go running.
 From the fact that for all x_14, if x_14 were a writer, then x_14 is a politician, and that for all x_14, if x_14 were a politician, then x_14 is a writer we can infer that for all x_14, x_14 is a writer if and only if x_14 is a politician via universal biconditional introduction. From the fact that for all x_14, x_14 is a writer if and only if x_14 is a politician, and that for all x_14, x_14 is not a writer we can infer that for all x_14, x_14 is not a politician via universal biconditional elimination. From the fact that there is at least one x_14 for which x_14 is a politician or x_14 will write a letter, and that for all x_14, x_14 is not a politician we can infer that there is at least one x_14 for which x_14 will write a letter via existential disjunctive syllogism. Finally, from the fact that there is at least one x_14 for which x_14 will write a letter we can infer that there is at least one x_14 for which x_14 will write a letter or x_14 will go running via existential addition, which contradicts that For all x_14, neither x_14 will write a letter nor x_14 will go running. Therefore, the answer is no.