Consider the following premises. For all x_8, x_8 will not climb a mountain. For all x_8, if x_8 were a politician, then x_8 is climbing a mountain. For all x_8, x_8 is a politician if and only if x_8 is a writer. Can we infer the following from them? For all x_8, x_8 is not a writer.
 From the fact that for all x_8, x_8 is a politician if and only if x_8 is a writer we can infer that for all x_8, if x_8 were a writer, then x_8 is a politician. From the fact that for all x_8, if x_8 were a writer, then x_8 is a politician, and that for all x_8, if x_8 were a politician, then x_8 is climbing a mountain we can infer that for all x_8, if x_8 were a writer, then x_8 is climbing a mountain. Finally, from the fact that for all x_8, if x_8 were a writer, then x_8 is climbing a mountain, and that for all x_8, x_8 will not climb a mountain we can infer that for all x_8, x_8 is not a writer. Therefore, the answer is yes.