Consider the following premises. Richard is not a cashier or William is a sailor. If Jennifer plays a game, then it is cloudy. Richard is a cashier or Jennifer is playing a game. It is cloudy if and only if William is a sailor. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that Richard is a cashier or Jennifer is playing a game, and that Richard is not a cashier or William is a sailor we can infer that Jennifer is playing a game or William is a sailor via resolution. From the fact that it is cloudy if and only if William is a sailor we can infer that if William were a sailor, then it is cloudy via biconditional elimination. Finally, from the fact that if Jennifer plays a game, then it is cloudy, that if William were a sailor, then it is cloudy, and that Jennifer is playing a game or William is a sailor we can infer that it is cloudy via disjunction elimination. Therefore, the answer is yes.