A ring of sets on a set 
is a nonempty set 
of subsets of 
that is closed under union and set difference. Thus, if 
, then 
and 
(Zusmanovich 2018, p. 2).
A ring of sets contains the empty set and is closed under intersection, since 
and 
. A ring of sets is an algebra
of sets on 
iff it contains 
.
