Answer to Question #223394 in Discrete Mathematics for Owass

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 type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set $(A, ≤)$ one represents each element of $A$ as a vertex in the plane and draws a line segment or curve that goes upward from $x$ to whenever $y$ covers $x$ (that is, whenever $x ≤ y$ and there is no $z$ such that $x ≤ z ≤ y$ ). These curves may cross each other but must not touch any vertices other than their endpoints. Such a diagram, with labeled vertices, uniquely determines its partial order.

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