Consider the following premises. If it is overcast, then it is not cold. If Sarah were bored, then it is cold. If Linda drives a car, then it is cold. Patricia is not a musician or Sarah is bored. Patricia is a musician or Linda is driving a car. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that Patricia is a musician or Linda is driving a car, and that Patricia is not a musician or Sarah is bored we can infer that Linda is driving a car or Sarah is bored via resolution. From the fact that if Linda drives a car, then it is cold, that if Sarah were bored, then it is cold, and that Linda is driving a car or Sarah is bored we can infer that it is cold via disjunction elimination. Finally, from the fact that if it is overcast, then it is not cold, and that it is cold we can infer that it is not overcast via modus tollens. Therefore, the answer is yes.