Distributive Lattice with Examples

In this class, we discuss Distributive Lattice with Examples.

The reader should have prior knowledge of lattice. Click here.

Distributive Law:

a Λ (b V c) = (a Λ b) V (a Λ c)

a V (b Λ c) = (a V b) Λ (a V c)

Distributive Lattice:

In a lattice, for all a, b, and c ∈ L. if the above two distributive laws satisfy, we say it is a distributive lattice.

Example 1:

The diagram below shows the distributive lattice.

c1 Λ (a1 V b1)

c1 Λ 1 = c1

(c1 Λ a1) V (c1 Λ b1)

0 V c1

c1

Example 2:

The diagram below shows the distributive lattice.