PROBLEM 4 For each relation, indicate whether the relation is: Reflexive, anti-reflexive, or neither Symmetric, anti-symmetric, or neither Transitive or not transitive Justify your answer. (a) The domain of the relation L is the set of all real numbers. For r, y € R, «Ly if z < y. (b) The domain of the relation A is the set of all real mumbers, xAy if |r-y| S 2 (c) The domain of the relation Z is the set of all real numbers. #Zy if y = 2x

PROBLEM 4 For each relation, indicate whether the relation is: Reflexive, anti-reflexive, or neither Symmetric, anti-symmetric, or neither Transitive or not transitive Justify your answer. (a) The domain of the relation L is the set of all real numbers. For r, y € R, «Ly if z < y. (b) The domain of the relation A is the set of all real mumbers, xAy if |r-y| S 2 (c) The domain of the relation Z is the set of all real numbers. #Zy if y = 2x

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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Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r, y) ry = 1} . Use a similar representation for each of your answers to the questions below, and write your answer in the accompanying box What is the composite relation R2 ? (a) (b) What is the composite relation R3? What is the composite relation R4? (c) (d) What is the transitive closure of R?
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