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#### Abbreviation: CdLat

### Definition

A *complemented lattice* is a bounded lattice *L* = (*L*,∨,0,∧,1) such that
every element has a complement: ∃*y*(*x*∨*y* = 1 and *x*∧*y* = 0).

### Morphisms

Let *L* and *M* be complemented lattices. A morphism from *L* to *M* is a function *h* : *L*→*M* that is a
bounded lattice homomorphism:
*h*(*x*∨*y*) = *h*(*x*)∨*h*(*y*) and *h*(*x*∧*y*) = *h*(*x*)∧*h*(*y*) and *h*(0) = 0 and *h*(1) = 1.

### Some results

### Examples

(*P*(*S*),∪,Ø,∩,*S*), the collection
of subsets of a set *S*, with union, empty set, intersection, and the whole
set *S*.

### Properties

### Finite members

[Size 1]?: 1

[Size 2]?: 1

[Size 3]?: 0

[Size 4]?: 1

[Size 5]?: 2

[Size 6]?:

[Size 7]?:

[Size 8]?:

### Subclasses

Complemented modular lattices

### Superclasses

Bounded lattices