Archangel Macsika
Let X = {1, 2, 3, 4, 6, 8, 12, 24} and R be a division relation defined on X. Find the Hasse diagram of the poset.
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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 (X, R) one represents each element of X as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x (that is, whenever x ≤ y and there is no z such that x ≤ z ≤ y).
In our case, the Hasse diagram is the following: