Digramatic Representation Of Partial Order Relations And Posets

DIAGRAMMATIC REPRESENTATION OF PARTIAL ORDER RELATIONS AND POSETS: In the previous chapter, we have seen the diagraph of a relation. In
this section, we use the diagraphs of the partial order relations, to represent the relations in a very suitable way known as Hasse diagram. We understand the Hasse diagrame, using following example.

Example : Let A = {a, b, c, d, e} and the following diagram represents the diagraph of the partial order relation on A.

Now, we shall draw Hasse diagram from the above diagrams using following rules.
(i) Drop the reflexive loops

(ii) Drop transitive lines

(iii) Drop arrows