Consider the following premises. If Patricia were a lawyer, then it is late. If it rains, then Patricia is a lawyer. If Linda were a doctor, then it is raining. If David sleeps, then it is raining. Linda is a doctor or David is sleeping. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that if Linda were a doctor, then it is raining, that if David sleeps, then it is raining, and that Linda is a doctor or David is sleeping we can infer that it is raining via disjunction elimination. From the fact that if it rains, then Patricia is a lawyer, and that it is raining we can infer that Patricia is a lawyer via modus ponens. Finally, from the fact that if Patricia were a lawyer, then it is late, and that Patricia is a lawyer we can infer that it is late via modus ponens. Therefore, the answer is yes.