Consider the following premises. Robert is running or Joseph is playing a game. James is not reading a book. If William works, then James is reading a book. If Robert goes running, then William is working. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not playing a game.
 From the fact that if Robert goes running, then William is working, and that if William works, then James is reading a book we can infer that if Robert goes running, then James is reading a book via transitivity. From the fact that if Robert goes running, then James is reading a book, and that James is not reading a book we can infer that Robert is not running via modus tollens. Finally, from the fact that Robert is running or Joseph is playing a game, and that Robert is not running we can infer that Joseph is playing a game via disjunctive syllogism, which contradicts that Joseph is not playing a game. Therefore, the answer is no.