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4 points). For each of the following relations ~ on the integers Z, say whether ~ is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/ ~. a.~y if and only if x ≤ y. b. xy if and only if x - y is even.

4 points). For each of the following relations ~ on the integers Z, say whether ~ is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/ ~. a.~y if and only if x ≤ y. b. xy if and only if x - y is even.

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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2007 aisiga yi Y TAT- X tad (ainlog S) 01 moldor Home) por x = (10¹0) (co) phodami ned (X)V dorg boodtoddylon sit dotel2.8 (X)32 to moitqib tollyzo movi) d orgab ametall olgaie od word to i styme sult to shooted alf shirqato.b (0.1) (0,0)) = 7 salida boonstelbarednak odt stets dien 1.V. dgg boodtoddgion ort bisla.s X)0 to moitish thike as evid lo sgorgash belgisoras odd wa qub an-0 bestelboran sila svi b points). For each of the following relations Problem (4 on the integers Z, say whether is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x < y. b. xy if and only if x - y is even.
Transcribed Image Text:2007 aisiga yi Y TAT- X tad (ainlog S) 01 moldor Home) por x = (10¹0) (co) phodami ned (X)V dorg boodtoddylon sit dotel2.8 (X)32 to moitqib tollyzo movi) d orgab ametall olgaie od word to i styme sult to shooted alf shirqato.b (0.1) (0,0)) = 7 salida boonstelbarednak odt stets dien 1.V. dgg boodtoddgion ort bisla.s X)0 to moitish thike as evid lo sgorgash belgisoras odd wa qub an-0 bestelboran sila svi b points). For each of the following relations Problem (4 on the integers Z, say whether is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x < y. b. xy if and only if x - y is even.
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