Consider the following premises. If Michael drinks water, then Jennifer is a sailor. If Jennifer were a sailor, then James is sleeping. If James sleeps, then Michael is drinking water. If James sleeps, then Jennifer is a sailor. Can we infer the following from them? If we can, name the inference rule being used: If is not true that James is sleeping if and only if Jennifer is a sailor.
 From the fact that if James sleeps, then Michael is drinking water, and that if Michael drinks water, then Jennifer is a sailor we can infer that if James sleeps, then Jennifer is a sailor via transitivity. From the fact that if Jennifer were a sailor, then James is sleeping, and that if James sleeps, then Jennifer is a sailor we can infer that Jennifer is a sailor if and only if James is sleeping via biconditional introduction. From the fact that Jennifer is a sailor if and only if James is sleeping we can infer that if Jennifer were a sailor, then James is sleeping via biconditional elimination. Finally, from the fact that if James sleeps, then Jennifer is a sailor, and that if Jennifer were a sailor, then James is sleeping we can infer that James is sleeping if and only if Jennifer is a sailor via biconditional introduction, which contradicts that If is not true that James is sleeping if and only if Jennifer is a sailor. Therefore, the answer is no.