Consider the following premises. For all x_2, x_2 will read a book if and only if x_2 is an artist. There is at least one x_2 for which x_2 will read a book. For all x_2, x_2 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, either x_2 is a nurse or x_2 is an artist are not true.
 From the fact that for all x_2, x_2 will read a book if and only if x_2 is an artist we can infer that for all x_2, if x_2 reads a book, then x_2 is an artist via universal biconditional elimination. From the fact that for all x_2, if x_2 reads a book, then x_2 is an artist, and that there is at least one x_2 for which x_2 will read a book we can infer that there is at least one x_2 for which x_2 is an artist via existential modus ponens. Finally, from the fact that for all x_2, x_2 is a nurse, and that there is at least one x_2 for which x_2 is an artist we can infer that there is at least one x_2 for which x_2 is a nurse and x_2 is an artist via existential conjunction, which contradicts that For all x_2, either x_2 is a nurse or x_2 is an artist are not true. Therefore, the answer is no.