Consider the following premises. Joseph is taking a plane if and only if Jessica is playing a game. Joseph is taking a plane or William is an office clerk. Jessica is playing a game or Jessica is not bored. If William were an office clerk, then Jessica is bored. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not playing a game.
 From the fact that Jessica is playing a game or Jessica is not bored we can infer that if Jessica were bored, then Jessica is playing a game via rewriting. From the fact that if William were an office clerk, then Jessica is bored, and that if Jessica were bored, then Jessica is playing a game we can infer that if William were an office clerk, then Jessica is playing a game via transitivity. From the fact that Joseph is taking a plane if and only if Jessica is playing a game we can infer that if Joseph takes a plane, then Jessica is playing a game via biconditional elimination. Finally, from the fact that if Joseph takes a plane, then Jessica is playing a game, that if William were an office clerk, then Jessica is playing a game, and that Joseph is taking a plane or William is an office clerk we can infer that Jessica is playing a game via disjunction elimination, which contradicts that Jessica is not playing a game. Therefore, the answer is no.