CSNB 143 Discrete Mathematical Structures Chapter 9 – Poset

POSET OBJECTIVES Student should be able to understand the concept used in dictionary. Students should be able to apply poset in daily lives that involves order. Students should be able to create order by themselves.

What, Which, Where, When Basics of set Its criteria (Clear / Not Clear) Terms used in poset (Clear / Not Clear) Hasse Diagram (Clear / Not Clear) Topological Sorting (Clear / Not Clear)

PARTIALLY ORDERED SETS (POSET) A relation R on set A is called Partial Order if R is reflexive, antisymmetric and transitive. In short, it is called Poset, written as (A, R) where R is a relation that turns A to a poset. Poset is being used widely in comparison matters such as a dictionary. Ex 1: Let say set S = {a, b, c,… z} is an ordered set. Then set S* is a set for all possibility of words in various length, either it is meaningful or not. So we can get

help < helping In S* because help < help in s5. And also helper < helping because helpe < helpi in s5. Using this comparison, a dictionary was introduced. Theorem: A diagraph for poset has no cycle length more that 1.

Hasse Diagram Let A is a finite set. To draw a diagraph for poset, we must consider three things: Graph has no cycle length 1 (irreflexive). Graph is not transitive for all vertices. Graf has no arrow (always pointing upwards) This particular graph is called a Hasse Diagram. Hasse Diagram is one of the methods to represent poset.

Ex2: Consider a diagraph below: Then, consider the things to make it a Hasse Diagram. B C A