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===Completeness===
The laws listed above define Boolean algebra, in the sense that they entail the rest of the subject. The laws ''complementation'' 1 and 2, together with the monotone laws, suffice for this purpose and can therefore be taken as one possible ''complete'' set of laws or [[axiomatization]] of Boolean algebra. Every law of Boolean algebra follows logically from these axioms. Furthermore, Boolean algebras can then be defined as the [[model (logic)|models]] of these axioms as treated in ''{{section link|#Boolean algebras}}''.

Writing down further laws of Boolean algebra cannot give rise to any new consequences of these axioms, nor can it rule out any model of them. In contrast, in a list of some but not all of the same laws, there could have been Boolean laws that did not follow from those on the list, and moreover there would have been models of the listed laws that were not Boolean algebras.

This axiomatization is by no means the only one, or even necessarily the most natural given that attention was not paid as to whether some of the axioms followed from others, but there was simply a choice to stop when enough laws had been noticed, treated further in ''{{section link|#Axiomatizing Boolean algebra}}''. Or the intermediate notion of axiom can be sidestepped altogether by defining a Boolean law directly as any ''tautology'', understood as an equation that holds for all values of its variables over 0 and 1.<ref name="McGee_2005"/><ref name="Goodstein_2012"/> All these definitions of Boolean algebra can be shown to be equivalent.