Complemented lattice

In the mathematical discipline of order theory, and in particular, in lattice theory, a complemented lattice is a bounded lattice in which each element x has a complement, defined as a unique element ~ x such that

$x\wedge\sim x=0$

and

$x\vee\sim x=1.$

A Boolean algebra may be defined as a complemented distributive lattice.

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Complemented lattice

See also: Complemented lattice, Boolean algebra, Distributive lattice, Lattice (order), Mathematics, Order theory