Consider the following premises. Susan is cooking if and only if it is overcast. If Jessica plays a game, then Susan is cooking. If Susan cooks, then Jessica is playing a game. Can we infer the following from them? The fact that it is overcast does not imply that Jessica is playing a game.
 From the fact that if Jessica plays a game, then Susan is cooking, and that if Susan cooks, then Jessica is playing a game we can infer that Jessica is playing a game if and only if Susan is cooking. From the fact that Jessica is playing a game if and only if Susan is cooking we can infer that if Susan cooks, then Jessica is playing a game. From the fact that Susan is cooking if and only if it is overcast we can infer that if it is overcast, then Susan is cooking. Finally, from the fact that if it is overcast, then Susan is cooking, and that if Susan cooks, then Jessica is playing a game we can infer that if it is overcast, then Jessica is playing a game, which contradicts that The fact that it is overcast does not imply that Jessica is playing a game. Therefore, the answer is no.