Consider the following premises. Elisabeth is playing a game or it is not raining. Elisabeth is not playing a game. If Elisabeth plays a game, then it is raining. It is raining if and only if Karen is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Karen is climbing a mountain.
 From the fact that Elisabeth is playing a game or it is not raining we can infer that if it rains, then Elisabeth is playing a game via rewriting. From the fact that if it rains, then Elisabeth is playing a game, and that if Elisabeth plays a game, then it is raining we can infer that it is raining if and only if Elisabeth is playing a game via biconditional introduction. From the fact that it is raining if and only if Elisabeth is playing a game, and that Elisabeth is not playing a game we can infer that it is not raining via biconditional elimination. From the fact that it is raining if and only if Karen is climbing a mountain we can infer that if Karen climbs a mountain, then it is raining via biconditional elimination. Finally, from the fact that if Karen climbs a mountain, then it is raining, and that it is not raining we can infer that Karen is not climbing a mountain via modus tollens, which contradicts that Karen is climbing a mountain. Therefore, the answer is no.