Consider the following premises. Karen is playing a game if and only if James is climbing a mountain. William is not working. William is working or Karen is not playing a game. Can we infer the following from them? James is climbing a mountain.
 From the fact that William is working or Karen is not playing a game we can infer that if Karen plays a game, then William is working. From the fact that if Karen plays a game, then William is working, and that William is not working we can infer that Karen is not playing a game. Finally, from the fact that Karen is playing a game if and only if James is climbing a mountain, and that Karen is not playing a game we can infer that James is not climbing a mountain, which contradicts that James is climbing a mountain. Therefore, the answer is no.