Consider the following premises. For all x_16, x_16 is a politician if and only if x_16 is an electrician. For all x_16, if x_16 were a politician, then x_16 is a carpenter. For all x_16, x_16 is not a carpenter. For all x_16, if x_16 cooks, then x_16 is an electrician. For all x_16, if x_16 writes a letter, then x_16 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 will not write a letter.
 From the fact that for all x_16, x_16 is a politician if and only if x_16 is an electrician we can infer that for all x_16, if x_16 were an electrician, then x_16 is a politician via universal biconditional elimination. From the fact that for all x_16, if x_16 were a politician, then x_16 is a carpenter, and that for all x_16, x_16 is not a carpenter we can infer that for all x_16, x_16 is not a politician via universal modus tollens. From the fact that for all x_16, if x_16 cooks, then x_16 is an electrician, and that for all x_16, if x_16 were an electrician, then x_16 is a politician we can infer that for all x_16, if x_16 cooks, then x_16 is a politician via universal transitivity. From the fact that for all x_16, if x_16 cooks, then x_16 is a politician, and that for all x_16, x_16 is not a politician we can infer that for all x_16, x_16 will not cook via universal modus tollens. Finally, from the fact that for all x_16, if x_16 writes a letter, then x_16 is cooking, and that for all x_16, x_16 will not cook we can infer that for all x_16, x_16 will not write a letter via universal modus tollens. Therefore, the answer is yes.