Consider the following premises. Linda is not bored. For all y, y will write a letter. Robert is sleeping if and only if Linda is bored. If Robert doesn't sleep, then James is making tea. Can we infer the following from them? If we can, name the inference rule being used: James is not making tea.
 From the fact that Robert is sleeping if and only if Linda is bored, and that Linda is not bored we can infer that Robert is not sleeping via biconditional elimination. Finally, from the fact that if Robert doesn't sleep, then James is making tea, and that Robert is not sleeping we can infer that James is making tea via modus ponens, which contradicts that James is not making tea. Therefore, the answer is no.