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12. Let A be the set of all integers = {..-3,-2,-1,0,1,2,3,...}. Define the relation R on A as follows: (x,y) e R if and only if x - y = 1. In each part, answer yes or no. If yes, then explain why in terms of this specific relation about absolute value (not just by stating the generic definition of the property). If you say no, give a specific counterexample to explain why. a) Is R reflexive?

12. Let A be the set of all integers = {..-3,-2,-1,0,1,2,3,...}. Define the relation R on A as follows: (x,y) e R if and only if x - y = 1. In each part, answer yes or no. If yes, then explain why in terms of this specific relation about absolute value (not just by stating the generic definition of the property). If you say no, give a specific counterexample to explain why. a) Is R reflexive?

Advanced Engineering Mathematics
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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12. Let A be the set of all integers = {....-3,-2,-1,0,1,2,3,...}. Define the relation R on A as follows: (x,y) E R if and only if |x - y = 1. In each part, answer yes or no. If yes, then explain why in terms of this specific relation about absolute value (not just by stating the generic definition of the property). If you say no, give a specific counterexample to explain why. a) Is R reflexive? b) Is R symmetric? c) Is R antisymmetric? d) Is R transitive?
Transcribed Image Text:12. Let A be the set of all integers = {....-3,-2,-1,0,1,2,3,...}. Define the relation R on A as follows: (x,y) E R if and only if |x - y = 1. In each part, answer yes or no. If yes, then explain why in terms of this specific relation about absolute value (not just by stating the generic definition of the property). If you say no, give a specific counterexample to explain why. a) Is R reflexive? b) Is R symmetric? c) Is R antisymmetric? d) Is R transitive?
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