Answer to Question #147483 in Discrete Mathematics for Promise Omiponle

Question

Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).

Answer 1

In order theory, 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 (S, ⪯) one represents each element of S as a vertex in the plane and draws a line segment or vector 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). These lines 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, the Hasse diagram is the following: