Consider the following premises. William is not an astronaut. Robert is a janitor or Joseph is an electrician. Karen is not a writer or Michael is sleeping. William is an astronaut if and only if Robert is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Joseph is an electrician or Michael is sleeping.
 From the fact that William is an astronaut if and only if Robert is a janitor, and that William is not an astronaut we can infer that Robert is not a janitor via biconditional elimination. From the fact that Robert is not a janitor we can infer that Robert is not a janitor or Karen is a writer via addition. From the fact that Robert is not a janitor or Karen is a writer, and that Robert is a janitor or Joseph is an electrician we can infer that Karen is a writer or Joseph is an electrician via resolution. Finally, from the fact that Karen is a writer or Joseph is an electrician, and that Karen is not a writer or Michael is sleeping we can infer that Joseph is an electrician or Michael is sleeping via resolution. Therefore, the answer is yes.