Consider the following premises. It is not cloudy or Barbara is writing a letter. It is cloudy or Patricia is climbing a mountain. For all y_2, y_2 will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not writing a letter.
 From the fact that for all y_2, y_2 will not climb a mountain we can infer that Patricia is not climbing a mountain via universal instantiation. From the fact that it is cloudy or Patricia is climbing a mountain, and that it is not cloudy or Barbara is writing a letter we can infer that Patricia is climbing a mountain or Barbara is writing a letter via resolution. Finally, from the fact that Patricia is climbing a mountain or Barbara is writing a letter, and that Patricia is not climbing a mountain we can infer that Barbara is writing a letter via disjunctive syllogism, which contradicts that Barbara is not writing a letter. Therefore, the answer is no.