Consider the following premises. William is poor if and only if Robert is a bartender. If James makes tea, then William is poor. Robert is a bartender or James is making tea. Can we infer the following from them? If we can, name the inference rule being used: William is not poor.
 From the fact that William is poor if and only if Robert is a bartender we can infer that if Robert were a bartender, then William is poor via biconditional elimination. Finally, from the fact that if Robert were a bartender, then William is poor, that if James makes tea, then William is poor, and that Robert is a bartender or James is making tea we can infer that William is poor via disjunction elimination, which contradicts that William is not poor. Therefore, the answer is no.