Consider the following premises. Jessica is working or it is not windy. Jessica is working if and only if John is climbing a mountain. Can we infer the following from them? The fact that it is windy does not imply that John is climbing a mountain.
 From the fact that Jessica is working or it is not windy we can infer that if it is windy, then Jessica is working. From the fact that Jessica is working if and only if John is climbing a mountain we can infer that if Jessica works, then John is climbing a mountain. Finally, from the fact that if it is windy, then Jessica is working, and that if Jessica works, then John is climbing a mountain we can infer that if it is windy, then John is climbing a mountain, which contradicts that The fact that it is windy does not imply that John is climbing a mountain. Therefore, the answer is no.