Consider the following premises. For all z_4, z_4 will read a book if and only if z_4 will write a letter. There is at least one z_4 for which z_4 is not a writer. For all z_4, z_4 will write a letter or z_4 is an electrician. For all z_4, z_4 will read a book if and only if z_4 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all z_4, z_4 is not an electrician.
 From the fact that for all z_4, z_4 will read a book if and only if z_4 is a writer, and that there is at least one z_4 for which z_4 is not a writer we can infer that there is at least one z_4 for which z_4 will not read a book via existential biconditional elimination. From the fact that for all z_4, z_4 will read a book if and only if z_4 will write a letter, and that there is at least one z_4 for which z_4 will not read a book we can infer that there is at least one z_4 for which z_4 will not write a letter via existential biconditional elimination. Finally, from the fact that for all z_4, z_4 will write a letter or z_4 is an electrician, and that there is at least one z_4 for which z_4 will not write a letter we can infer that there is at least one z_4 for which z_4 is an electrician via existential disjunctive syllogism, which contradicts that For all z_4, z_4 is not an electrician. Therefore, the answer is no.