example of Boolean algebras
In , let be the collection of all finite subsets of , and the collection of all cofinite subsets of . Then is a Boolean algebra.
More generally, any field of sets is a Boolean algebra. In particular, any sigma algebra in a set is a Boolean algebra.
More generally, if we have a collection of Boolean algebras , indexed by a set , then is a Boolean algebra, where the Boolean operations are defined componentwise.
In particular, if is a Boolean algebra, then set of functions from some non-empty set to is also a Boolean algebra, since .
Let be a set, and be the set of all -ary relations on . Then is a Boolean algebra under the usual set-theoretic operations. The easiest way to see this is to realize that , the powerset of the -fold power of .
|Title||example of Boolean algebras|
|Date of creation||2013-03-22 17:52:33|
|Last modified on||2013-03-22 17:52:33|
|Last modified by||CWoo (3771)|