Consider the following premises. Joseph is working if and only if David is not playing a game. David is playing a game if and only if Jennifer is writing a letter. Jennifer is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Joseph is working.
 From the fact that David is playing a game if and only if Jennifer is writing a letter, and that Jennifer is not writing a letter we can infer that David is not playing a game via biconditional elimination. From the fact that Joseph is working if and only if David is not playing a game we can infer that if David doesn't play a game, then Joseph is working via biconditional elimination. Finally, from the fact that if David doesn't play a game, then Joseph is working, and that David is not playing a game we can infer that Joseph is working via modus ponens. Therefore, the answer is yes.