Consider the following premises. For all y_3, y_3 will not play a game. It is cold if and only if Linda is playing a game. It is cold. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is a scientist.
 From the fact that it is cold we can infer that it is cold or Elisabeth is a scientist via addition. From the fact that for all y_3, y_3 will not play a game we can infer that Linda is not playing a game via universal instantiation. From the fact that it is cold if and only if Linda is playing a game, and that Linda is not playing a game we can infer that it is not cold via biconditional elimination. Finally, from the fact that it is cold or Elisabeth is a scientist, and that it is not cold we can infer that Elisabeth is a scientist via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.