Solution to Let A = {1, 2, 3, 6, 12} and R = {(a, b)/a,b A and … - Sikademy
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Archangel Macsika

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

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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:

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Question ID: mtid-5-stid-8-sqid-1407-qpid-1145