A complete product for a finite family 
of subsets of a fixed
universal set 
is an intersection of the
form
 |
(1)
|
where 
is a nonnegative integer and each 
is either 
or its complement 
. There are 
formal choices, some of which may give the empty
set. For 
,
the single complete product is 
. For example, the 
formal complete products of 
are
 |
(2)
|
The nonempty complete products are pairwise disjoint and partition 
. Each element of the generated Boolean
algebra has a unique representation, up to order, as a union
of these nonempty complete products, with the empty set
represented by the empty union. In the following example,
denotes symmetric
difference, which agrees with union for disjoint complete
products:
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
(Comtet 1974, p. 186).
