Consider the following premises. If Jessica were happy, then it is raining. If it rains, then James is a lawyer. If William were a politician, then Patricia is playing a game. If James were a lawyer, then William is a politician. Can we infer the following from them? If Jessica were happy, then Patricia is playing a game.
 From the fact that if it rains, then James is a lawyer, and that if James were a lawyer, then William is a politician we can infer that if it rains, then William is a politician. From the fact that if Jessica were happy, then it is raining, and that if it rains, then William is a politician we can infer that if Jessica were happy, then William is a politician. Finally, from the fact that if Jessica were happy, then William is a politician, and that if William were a politician, then Patricia is playing a game we can infer that if Jessica were happy, then Patricia is playing a game. Therefore, the answer is yes.