Consider the following premises. If Jessica were a janitor, then it is sunny. John is a bartender if and only if William is climbing a mountain. If John were a bartender, then Jessica is a janitor. If it is sunny, then William is climbing a mountain. Can we infer the following from them? The fact that William climbs a mountain does not imply that Jessica is a janitor.
 From the fact that John is a bartender if and only if William is climbing a mountain we can infer that if William climbs a mountain, then John is a bartender. From the fact that if Jessica were a janitor, then it is sunny, and that if it is sunny, then William is climbing a mountain we can infer that if Jessica were a janitor, then William is climbing a mountain. Finally, from the fact that if William climbs a mountain, then John is a bartender, and that if John were a bartender, then Jessica is a janitor we can infer that if William climbs a mountain, then Jessica is a janitor, which contradicts that The fact that William climbs a mountain does not imply that Jessica is a janitor. Therefore, the answer is no.