Simple category theory question

I was hoping somebody could help me understand a remark in Lawvere and
Schanuel's book *Conceptual Mathematics*.

On p180, the authors say that one can investigate a large category X
by considering the mappings between X and a small category C. To
illustrate this, they say that one can take as C the category whose
objects are the sets 1 = {0} and 2 = {0,1}, and whose morphisms are
the 8 set-functions whose domain and codomain are among these
objects. Then, one can take the maps 1->X as the points of X; the
maps 2->X as the pairs of points of X; the maps X->2 as yes/no
properties of points of X; the operation subtracting-from-1 on 2 as
negation, etc.

After this they make the remark I don't get: if we add a three-point
set to C (getting a category with 56 maps), then conjunction and
disjunction become internal to C.

Can someone help me see how this would go? Thanks!

Max Weiss
.