Consider the following premises. Karen is not excited. It is cold or it is raining. It is not cold or Karen is excited. It is not raining or Charles is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Charles is not a carpenter.
 From the fact that it is cold or it is raining, and that it is not cold or Karen is excited we can infer that it is raining or Karen is excited via resolution. From the fact that it is raining or Karen is excited, and that it is not raining or Charles is a carpenter we can infer that Karen is excited or Charles is a carpenter via resolution. Finally, from the fact that Karen is excited or Charles is a carpenter, and that Karen is not excited we can infer that Charles is a carpenter via disjunctive syllogism, which contradicts that Charles is not a carpenter. Therefore, the answer is no.