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) |
