Sub Lattice with an Example

In this class, We discuss Sub Lattice with an Example.

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

Sub Lattice:

A non-empty subset S of a lattice [L, V, Λ] is called a sublattice if and only if S is closed under the operation Λ and V.

Another way to understand:

If a, b ∈ S, then a V b ∈ S and a Λ b ∈ S. for all a,b belongs to S.

Example:

The diagram below shows the hasse diagram.

The set S = {s1, s2, s4, s6} is a sub lattice.

The set S1 = {s1, s5, s7, s8} is not a sublattice.