Consider the following premises. James is not sad. If Jessica were an astronaut, then it is raining. If it rains, then Jessica is an astronaut. If Jessica were an astronaut, then James is sad. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that if Jessica were an astronaut, then James is sad, and that James is not sad we can infer that Jessica is not an astronaut via modus tollens. From the fact that if Jessica were an astronaut, then it is raining, and that if it rains, then Jessica is an astronaut we can infer that Jessica is an astronaut if and only if it is raining via biconditional introduction. Finally, from the fact that Jessica is an astronaut if and only if it is raining, and that Jessica is not an astronaut we can infer that it is not raining via biconditional elimination, which contradicts that It is raining. Therefore, the answer is no.