Answer to Question #290602 in Discrete Mathematics for Govardhan

Question #290602

Draw hasse diagram representing the positive divisor of 36 and show digraph to It?

1
Expert's answer
2022-01-25T17:08:04-0500

a divides a so the relation R is reflexive. If a,ba,b are positive integers then, if aba|b then clearly, bab\nmid a . Hence the relation is not symmetric. Now abb=axa|b\Rightarrow b=ax for some integer x.x. Again bcc=byb|c\Rightarrow c=by for some integer y. Hence c=axyc=axy and so ac.a|c. Hence the relation is transitive. So the relation is a partial order relation and the set is a poset. Also its not totally ordered since 4,9 are non comparable.

Now its not a lattice since 494\vee 9 doesn't exist. since their least upper bound must be divisible by both 4 and 9 and no such element exist.

The Hasse Diagram is below:


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