Disjoint sets 
and 
are sets whose
intersection 
, where 
is the empty set. 
sets 
, 
,
..., 
are disjoint if 
for 
.
For example, 
and 
are disjoint, but 
and 
are not. Disjoint sets are also said to be mutually exclusive. In the set-theoretic
terminology used here, they are also called independent
sets.
This set-theoretic terminology differs from independent events in probability. For disjoint events 
and 
in a common probability space,
. If both probabilities
are positive, then 
, so the events
are not independent. If at least one has probability zero, the product identity does hold (Grinstead
and Snell 2006, p. 140).
