Let X be a set and R a relation on X. Define R to be the reverse relation, so that (z, y) e R if and only if (y, z) e R. (a) What does it mean that Ris a strict partial order on X. (b) Show that R is a strict partial order if R is. (c) Let X = {1,2,..., 12} and define R by strict divisibility. Sketch (X, R) and (X, R). (d) Distinguish (X, R) and (X,R) or show that they are (essentially) the same, in the sense that there is an order preserving bijection between them.

Let X be a set and R a relation on X. Define R to be the reverse relation, so that (z, y) e R if and only if (y, z) e R. (a) What does it mean that Ris a strict partial order on X. (b) Show that R is a strict partial order if R is. (c) Let X = {1,2,..., 12} and define R by strict divisibility. Sketch (X, R) and (X, R). (d) Distinguish (X, R) and (X,R) or show that they are (essentially) the same, in the sense that there is an order preserving bijection between them.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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