Consider the following premises. For all x_7, x_7 will read a book. For all x_7, if x_7 were a carpenter, then x_7 is a politician. There is at least one x_7 for which x_7 is a carpenter. For all x_7, if x_7 reads a book, then x_7 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, either x_7 is a politician or x_7 is an electrician are not true.
 From the fact that for all x_7, if x_7 were a carpenter, then x_7 is a politician, and that there is at least one x_7 for which x_7 is a carpenter we can infer that there is at least one x_7 for which x_7 is a politician via existential modus ponens. From the fact that for all x_7, if x_7 reads a book, then x_7 is an electrician, and that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 is an electrician via universal modus ponens. Finally, from the fact that there is at least one x_7 for which x_7 is a politician, and that for all x_7, x_7 is an electrician we can infer that there is at least one x_7 for which x_7 is a politician and x_7 is an electrician via existential conjunction, which contradicts that For all x_7, either x_7 is a politician or x_7 is an electrician are not true. Therefore, the answer is no.