Consider the following premises. It is cloudy or Jessica is making tea. If Jessica makes tea, then James is playing squash. Joseph is a writer or James is not playing squash. If it is cloudy, then James is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Joseph is a writer.
 From the fact that if it is cloudy, then James is playing squash, that if Jessica makes tea, then James is playing squash, and that it is cloudy or Jessica is making tea we can infer that James is playing squash via disjunction elimination. From the fact that Joseph is a writer or James is not playing squash we can infer that if James plays squash, then Joseph is a writer via rewriting. Finally, from the fact that if James plays squash, then Joseph is a writer, and that James is playing squash we can infer that Joseph is a writer via modus ponens. Therefore, the answer is yes.