A full dichotomy on all
points can have a "twin" dichotomy (also on all
points) that is identical to it except for the last bit, where it differs so one dichotomy ends with
and the other ends with
. It is those "twin" dichotomies that end up in the set
(both of them); the one ending with
goes to
and the one ending with
goes to
. Each of
and
has
elements, hence
which is their union has
elements.
The dichotomies that do not have a "twin" are the ones that end up in
and there are
of them. Each dichotomy goes to one, and only one, of the sets
,
,
. I hope this clarifies the matter. Please feel free to ask further questions.