Inclusion (Boolean algebra)

In Boolean algebra (structure), the inclusion relation ${\displaystyle a\leq b}$ is defined as ${\displaystyle ab'=0}$ and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order.

The inclusion relation ${\displaystyle a<b}$ 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 { (0,0), (0,1), (1,1) }.

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