Consider the following premises. Elisabeth is bored or Sarah is not rich. It is raining. Sarah is rich. Can we infer the following from them? If we can, name the inference rule being used: It is raining and Elisabeth is bored.
 From the fact that Elisabeth is bored or Sarah is not rich we can infer that if Sarah were rich, then Elisabeth is bored via rewriting. From the fact that if Sarah were rich, then Elisabeth is bored, and that Sarah is rich we can infer that Elisabeth is bored via modus ponens. Finally, from the fact that it is raining, and that Elisabeth is bored we can infer that it is raining and Elisabeth is bored via conjunction. Therefore, the answer is yes.