Answer to Question #234257 in Discrete Mathematics for mickey

Question

Draw the Hasse diagram for the “divides” relation on {2, 3, 5, 10, 11, 15, 25, 36, 42, 108}

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, $x<y$ if and only if $x|y.$ Therefore, the Hasse diagram is the following: