Consider the following premises. James is running if and only if William is happy. If it is windy, then Jennifer is climbing a mountain. If William were happy, then Jennifer is climbing a mountain. If Jennifer climbs a mountain, then William is happy. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is windy does not imply that James is running.
 From the fact that if Jennifer climbs a mountain, then William is happy, and that if William were happy, then Jennifer is climbing a mountain we can infer that Jennifer is climbing a mountain if and only if William is happy via biconditional introduction. From the fact that Jennifer is climbing a mountain if and only if William is happy we can infer that if Jennifer climbs a mountain, then William is happy via biconditional elimination. From the fact that James is running if and only if William is happy we can infer that if William were happy, then James is running via biconditional elimination. From the fact that if Jennifer climbs a mountain, then William is happy, and that if William were happy, then James is running we can infer that if Jennifer climbs a mountain, then James is running via transitivity. Finally, from the fact that if it is windy, then Jennifer is climbing a mountain, and that if Jennifer climbs a mountain, then James is running we can infer that if it is windy, then James is running via transitivity, which contradicts that The fact that it is windy does not imply that James is running. Therefore, the answer is no.