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a divides a so the relation R is reflexive. If are positive integers then, if then clearly, . Hence the relation is not symmetric. Now for some integer Again for some integer y. Hence and so 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 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: