Consider the following premises. For all x_10, x_10 will read a book if and only if x_10 is a nurse. For all x_10, x_10 will read a book or x_10 will listen to a song. For all x_10, x_10 is not a nurse. There is at least one x_10 for which x_10 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not listen to a song.
 From the fact that for all x_10, x_10 will read a book if and only if x_10 is a nurse, and that for all x_10, x_10 is not a nurse we can infer that for all x_10, x_10 will not read a book via universal biconditional elimination. Finally, from the fact that for all x_10, x_10 will read a book or x_10 will listen to a song, and that for all x_10, x_10 will not read a book we can infer that for all x_10, x_10 will listen to a song via universal disjunctive syllogism, which contradicts that For all x_10, x_10 will not listen to a song. Therefore, the answer is no.