Complement Set
Given a set
with a subset
, the complement of
is defined as
(1)
If
, then
(2)
where
is the
Empty Set
. Given a single
Set
, the second
Probability Axiom
gives
(3)
Using the fact that
,
(4)
(5)
This demonstrates that
(6)
Given two
Sets
,
(7)
(8)
© 1996-9
Eric W. Weisstein
1999-05-26