Construct Hasse or Poset Diagram

In this class, We discuss Construct Hasse or Poset Diagram.

The reader should have prior knowledge of a partially ordered set. Click Here.

Hasse or POSET Diagram:

Take a partially ordered set.

For a partially ordered set, we construct a hasse diagram.

The below conditions are followed to construct a hasse diagram.

1) create a vertex for each element in the POSET.

2) Construct an edge between two elements (a, b) if we do not find an element x such that aRx and xRb.

Example:

S = {Φ, {a}, {b}, {a,b}}

Relation R = [S, ⊆]

R ={(Φ, Φ), ({a},{a}), ({b}, {b}), ({a,b}, {a,b}), (Φ, {a}), (Φ, {b}), (Φ, {a,b}), ({a},{a,b}), ({b},{a,b})}

The diagram below shows the hasse diagram.

We do not have an edge in the diagram between (Φ, {a,b}).

There is an element {a} which satisfies (Φ, {a}) and ({a}, {a,b}). so no edge between (Φ, {a,b})