I know that propositional logic and Boolean algebra's are related in the sense that disjunction, conjunction and negation behave the same as join, meet and negation. Similarly, we also have union, intersection and complement when talking about sets. It's obvious that all these notions are closely related but I haven't seen a precise statement about this relation. I have also seen Boolean algebra's defined as orderd structures in which the order represents deducibility. This gives me the impression that the calculus of propositional logic can be replaced with a Boolean algebra and does this also hold for set arithmetic? Sorry if my question is too vague, but my understanding of this problem also is pretty vague. So any help would be appreciated.