Semi Lattice and Lattice with Examples

In this class, We discuss Semi Lattice and Lattice with Examples.

The reader should have prior knowledge of the least upper bound and greatest lower bound. Click Here.

Semi Lattices are of two types:

1) Join semilattice

Suppose the least upper bound exists for every pair of elements in a POSET. We call it join semilattice.

The diagram below shows the join semilattice.

2) Meet semilattice

Suppose the greatest lower bound exists for every pair of elements in a POSET. We call it join semilattice.

The diagram below shows the meet semilattice.

Lattice:

Suppose the least upper bound and greatest lower bound exist for every pair of elements in a POSET. We call it lattice.

The diagram below shows the lattice.