Given a set 
with a subset 
, the complement (denoted 
or 
) of 
with respect to 
is defined as
 |
(1)
|
Using set difference notation, the complement is defined by
 |
(2)
|
If 
, then
 |
(3)
|
where 
is the empty set. The complement is implemented in the
Wolfram Language as Complement[l,
l1, ...].
Given a single set, the second probability axiom gives
 |
(4)
|
Using the fact that 
,
 |
(5)
|
 |
(6)
|
This demonstrates that
 |
(7)
|
Given two sets,
 |  |  |
(8)
|
 |  |  |
(9)
|
