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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
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