Consider the following premises. If Robert plays a game, then Patricia is rich. Linda is a server. Linda is not a server. Can we infer the following from them? If we can, name the inference rule being used: Patricia is rich.
 From the fact that Linda is a server we can infer that Linda is a server or Robert is playing a game via addition. From the fact that Linda is a server or Robert is playing a game, and that Linda is not a server we can infer that Robert is playing a game via disjunctive syllogism. Finally, from the fact that if Robert plays a game, then Patricia is rich, and that Robert is playing a game we can infer that Patricia is rich via modus ponens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.