Consider the following premises. It is not cloudy. It is not raining. It is cloudy or it is raining. Can we infer the following from them? If we can, name the inference rule being used: Michael is sleeping.
 From the fact that it is cloudy or it is raining, and that it is not cloudy we can infer that it is raining via disjunctive syllogism. From the fact that it is raining we can infer that it is raining or Michael is sleeping via addition. Finally, from the fact that it is raining or Michael is sleeping, and that it is not raining we can infer that Michael is sleeping via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.