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