Question

Let L = {3, 4, 12, 24, 48, 82} and the relation < be defined on L such that x < y if x divides y. Draw the Hasse diagram.

Answer 1

 Let $L = \{3, 4, 12, 24, 48, 82\}$ and the relation < be defined on L such that x < y if x divides y. Let us draw the Hasse diagram.

The 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: