Consider the following premises. For all x, x is a writer if and only if x is fast. Robert is not a writer. Joseph is a musician or Robert is fast. Can we infer the following from them? If we can, name the inference rule being used: Joseph is a musician.
 From the fact that for all x, x is a writer if and only if x is fast we can infer that Robert is a writer if and only if Robert is fast via universal instantiation. From the fact that Robert is a writer if and only if Robert is fast, and that Robert is not a writer we can infer that Robert is not fast via biconditional elimination. From the fact that Joseph is a musician or Robert is fast we can infer that if Robert were not fast, then Joseph is a musician via rewriting. Finally, from the fact that if Robert were not fast, then Joseph is a musician, and that Robert is not fast we can infer that Joseph is a musician via modus ponens. Therefore, the answer is yes.