Hasse Diagram Divisibility. In this poset 60 is an upper bound though not a least upper. Then 24 is divisible by 3 4 and 12.
The hasse diagram representing the divisibility on the set will be computed as follows. Hence is a boolean algebra in this case. C 1 2 3 6 12 24 36 48.
Concretely for a partially ordered set one represents each element of s as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x.
If the number 1 is excluded while keeping divisibility as ordering on the elements greater than 1 then the resulting poset does not have a least element but any prime number is a minimal element for it. Since a partial order is reflexive hence each vertex of a must be related to itself so the edges from a vertex to itself are deleted in hasse diagram. So 2 will be connected to 4 and 6. Those elements are 2 3 and 5.
