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).