Consider the following premises. It is overcast or Charles is sleeping. Jessica is playing a game or it is not overcast. If Charles sleeps, then Jessica is playing a game. Can we infer the following from them? If we can, name the inference rule being used: Jessica is playing a game.
 From the fact that Jessica is playing a game or it is not overcast we can infer that if it is overcast, then Jessica is playing a game via rewriting. Finally, from the fact that if it is overcast, then Jessica is playing a game, that if Charles sleeps, then Jessica is playing a game, and that it is overcast or Charles is sleeping we can infer that Jessica is playing a game via disjunction elimination. Therefore, the answer is yes.