Answer to Question #223330 in Discrete Mathematics for Kofy

Question

Describe the Hasse diagram formed by the Relation "x is a divisor of y" for the set 
A = {1, 3, 6, 12, 24, 48}

Answer 1

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments are drawn between these points according to the following two rules:

1. If $x<y$ in the poset, then the point corresponding to $x$ appears lower in the drawing than the point corresponding to $y$.

2. The line segment between the points corresponding to any two elements $x$ and $y$ of the poset is included in the drawing iff $x$ covers $y$ or $y$ covers $x$ .

In our case, iff $x<y$ iff $x$ a divisor of $y.$ The Hasse diagram is the following: