Inclusion (Boolean algebra)
In Boolean algebra, the inclusion relation is defined as and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order.
The inclusion relation can be expressed in many ways:
The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set.
Some useful properties of the inclusion relation are:
The inclusion relation may be used to define Boolean intervals such that. A Boolean algebra whose carrier set is restricted to the elements in an interval is itself a Boolean algebra.
