Answered: 2. Let D be the set {xEZ I 2

Math

Advanced Math

2. Let D be the set {xEZ I 2

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

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2. Let D be the set {XEZI2<x<7} and relation M on D defined by: xMy → x and y have a common
factor AND x <y.
(a) Draw the directed graph of M.
2
7
(b) Is M reflexive? If not why not?
3
6
(c) Is M symmetric? If not why not?
5
(d) Is M antisymmetric? If not why not?
(g) If M is an equivalence relation, what are the
equivalence classes of M? (else write "n/a".)
(e) Is M transitive? If not why not?
(h) If M a partial order relation, then find a chain of
M. (else write "n/a".)
(f) Is M an equivalence relation, partial
order relation, neither, or both?

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