Consider the following premises. For all x_7, x_7 will not write a letter. For all x_7, x_7 is an electrician if and only if x_7 is a politician. For all x_7, x_7 will write a letter if and only if x_7 is an electrician. There is at least one x_7 for which x_7 is a politician if and only if x_7 is a writer. Can we infer the following from them? There is at least one x_7 for which x_7 is not a writer.
 From the fact that for all x_7, x_7 will write a letter if and only if x_7 is an electrician, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is not an electrician. From the fact that for all x_7, x_7 is an electrician if and only if x_7 is a politician, and that for all x_7, x_7 is not an electrician we can infer that for all x_7, x_7 is not a politician. Finally, from the fact that there is at least one x_7 for which x_7 is a politician if and only if x_7 is a writer, and that for all x_7, x_7 is not a politician we can infer that there is at least one x_7 for which x_7 is not a writer. Therefore, the answer is yes.