Consider the following premises. For all y_2, y_2 is a scientist if and only if y_2 will listen to a song. For all y_2, if y_2 listens to a song, then y_2 is a scientist. For all y_2, y_2 will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_2 for which y_2 is a scientist.
 From the fact that for all y_2, y_2 is a scientist if and only if y_2 will listen to a song we can infer that for all y_2, if y_2 were a scientist, then y_2 is listening to a song via universal biconditional elimination. From the fact that for all y_2, if y_2 were a scientist, then y_2 is listening to a song, and that for all y_2, if y_2 listens to a song, then y_2 is a scientist we can infer that for all y_2, y_2 is a scientist if and only if y_2 will listen to a song via universal biconditional introduction. Finally, from the fact that for all y_2, y_2 is a scientist if and only if y_2 will listen to a song, and that for all y_2, y_2 will not listen to a song we can infer that for all y_2, y_2 is not a scientist via universal biconditional elimination, which contradicts that There is at least one y_2 for which y_2 is a scientist. Therefore, the answer is no.