Consider the following premises. If Sarah were a politician, then William is bored. William is bored if and only if James is climbing a mountain. If William were bored, then Sarah is a politician. Can we infer the following from them? The fact that James climbs a mountain does not imply that Sarah is a politician.
 From the fact that William is bored if and only if James is climbing a mountain we can infer that if James climbs a mountain, then William is bored. From the fact that if William were bored, then Sarah is a politician, and that if Sarah were a politician, then William is bored we can infer that William is bored if and only if Sarah is a politician. From the fact that William is bored if and only if Sarah is a politician we can infer that if William were bored, then Sarah is a politician. Finally, from the fact that if James climbs a mountain, then William is bored, and that if William were bored, then Sarah is a politician we can infer that if James climbs a mountain, then Sarah is a politician, which contradicts that The fact that James climbs a mountain does not imply that Sarah is a politician. Therefore, the answer is no.