What Is Buerger's Disease?

In mathematics, a Boolean lattice is a type of lattice that is closely related to Boolean algebra. A complemented distributive lattice is called a Boolean lattice. A Boolean lattice <L, > can induce a Boolean algebra <L, ·, +, , 0, 1>, two binary operations can be defined in the Boolean <L, >, +: a · b = inf {a, b}, a + b = sup {a, b}, Since a Boolean is a bounded lattice, it must have the largest element and the smallest element, which are denoted as 1 and 0, respectively, and have a · 1 = a, a + 0 = a. Element a L, there is an element a L such that a · a = 0, a + a = 1, and since Boolean is a distributive lattice, there is a · (b + c) = (a · b) + (a · c), a + (b · c) = (a + b) · (a + c), so <L, ·, +, ', 0, 1> is induced by <L, > Boolean algebra ^[1] .

Bourg is

Complemented distributive lattice definition

Let <A, , , > be one

Theorem 1 assumes that <A, , , , > are arbitrary Booleans, then

,

The following ten laws hold ^[4] :

Conformity:

Idempotent law: aa = a

Law of exchange: ab = ba

Combination law: (ab) c = a (bc)

Distribution law: a (bc) = (ab) (ac)

Absorption law: a (ab) = a

The same law: a0 = a

Zero law: a1 = 1

Complementary law: a

= 1

De.Morgan Law:

Theorem 2 assumes that <A, , , , > is a Boolean lattice, between any atom a A and another non-zero element b A, there must be only a b or a 6 One of them was established ^[4] .

Theorem 3 suppose that <A, , , , > is a finite Boolean lattice, b A is any non-zero element, and at least one atom a A exists, so that a and b are on the same chain ^[4] .