If sets and are Independent, then so are
and , where is the complement of (i.e., the set of
all possible outcomes not contained in ). Let denote ``or'' and
denote ``and.'' Then
(1)
(2)
where is an abbreviation for . But and are independent, so
(3)
Also, since and are complements, they contain no common elements, which
means that
(4)
for any . Plugging (4) and (3) into (2) then gives