Answer to Question #248625 in Discrete Mathematics for Manoj

Question

Let A = {1, 2, 3, 6, 12} and R = {(a, b)/a,b A and “a divides b”}. Show that the relation R is a
partial order relation and also draw its Hasse diagram

Answer 1

A relation R on a set A is a partial order iff R is reflexive, antisymmetric and transitive. 

We have:

relation is reflexive: aRa - a divides a

relation is antisymmetric: aRb and bRa hold when a=b

relation is transitive: if aRb and bRc then aRc -if a divides b and b divides c then a divides c

So, the relation R is a partial order relation.

Hasse diagram: