I am a student doing your Traditional Logic book II and would like you answer a question that I have about disjunctive syllogisms. I would like to know the definition of an exclusive syllogism. I know that "either p or not p" is exclusive, but what about syllogisms like "Either Frodo destroys the ring or evil will triumph;Frodo destroyes the ring; therefore evil will not triumph." It seems to me that this statement is exclusive even though it's not in the "either p or not p" format. Only one or the other of these alternates can happen according to Lord of the Rings but it is invalid acording to logical rules. I would like you to tell me first if counts as an exclusive syllogism or not and then what the rules are for them. Thank you.