Consider the following premises. If Karen were a soldier, then David is an astronaut. If David were an astronaut, then James is writing a letter. If James writes a letter, then it is raining. If it rains, then Karen is a soldier. Can we infer the following from them? If we can, name the inference rule being used: If is not true that James is writing a letter if and only if David is an astronaut.
 From the fact that if James writes a letter, then it is raining, and that if it rains, then Karen is a soldier we can infer that if James writes a letter, then Karen is a soldier via transitivity. From the fact that if James writes a letter, then Karen is a soldier, and that if Karen were a soldier, then David is an astronaut we can infer that if James writes a letter, then David is an astronaut via transitivity. Finally, from the fact that if James writes a letter, then David is an astronaut, and that if David were an astronaut, then James is writing a letter we can infer that James is writing a letter if and only if David is an astronaut via biconditional introduction, which contradicts that If is not true that James is writing a letter if and only if David is an astronaut. Therefore, the answer is no.