Consider the following premises. If James were bored, then Joseph is not sad. For all y, y is sad. Patricia is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Patricia is playing tennis and James is not bored.
 From the fact that for all y, y is sad we can infer that Joseph is sad via universal instantiation. From the fact that if James were bored, then Joseph is not sad, and that Joseph is sad we can infer that James is not bored via modus tollens. Finally, from the fact that Patricia is playing tennis, and that James is not bored we can infer that Patricia is playing tennis and James is not bored via conjunction. Therefore, the answer is yes.