By the way, that makes a lot of sense despite perhaps being unintuitive at first. Every time you add an element to a set, the meet of that set gets “pushed farther down the poset”. So if the set is empty we need to start as far up as we can.

Similarly, AND of the empty set is True (there are no false elements!) and OR of the empty set is False (there are no true elements!).

Similarly, AND of the empty set is True (there are no false elements!) and OR of the empty set is False (there are no true elements!).