Boolean algebra (structure): Difference between revisions

Revision as of 01:12, 29 January 2006

Revision as of 02:44, 29 January 2006

Line 53:

|}

The first 3three pairs of axioms above: associativity, commutativity and absorption, mean that (''A'', <math>\land</math>, <math>\lor</math>) is a [[lattice (order)|lattice]]. Thus a Boolean algebra can also be equivalently defined as a [[distributive lattice|distributive]] [[complemented lattice]].

From these [[axioms]], one can show that the smallest element 0, the largest element 1, and the complement ¬''a'' of any element ''a'' are uniquely determined. For all ''a'' and ''b'' in ''A'', the following [[identity (mathematics)|identities]] also follow: