Consider the following premises. For all x_8, if x_8 were a nurse, then x_8 is playing a game. There is at least one x_8 for which x_8 will not play a game. For all x_8, x_8 is a nurse if and only if x_8 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is a scientist.
 From the fact that for all x_8, x_8 is a nurse if and only if x_8 is a scientist we can infer that for all x_8, if x_8 were a scientist, then x_8 is a nurse via universal biconditional elimination. From the fact that for all x_8, if x_8 were a scientist, then x_8 is a nurse, and that for all x_8, if x_8 were a nurse, then x_8 is playing a game we can infer that for all x_8, if x_8 were a scientist, then x_8 is playing a game via universal transitivity. Finally, from the fact that for all x_8, if x_8 were a scientist, then x_8 is playing a game, and that there is at least one x_8 for which x_8 will not play a game we can infer that there is at least one x_8 for which x_8 is not a scientist via existential modus tollens, which contradicts that For all x_8, x_8 is a scientist. Therefore, the answer is no.