Consider the relation R on R2 given by for any (a,b),(c,d)∈R 2, (a,b)R(c,d) if and only if a 2 +b 2=c 2 +d 2. (a) Prove that R is an equivalence relation on R 2. (b) Determine [(0,0)]
Consider the relation R on R2 given by for any (a,b),(c,d)∈R 2, (a,b)R(c,d) if and only if a 2 +b 2=c 2 +d 2. (a) Prove that R is an equivalence relation on R 2. (b) Determine [(0,0)]
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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Consider the relation R on R2 given by for any (a,b),(c,d)∈R 2, (a,b)R(c,d) if and only if a 2 +b 2=c 2 +d 2.
(a) Prove that R is an equivalence relation on R 2.
(b) Determine [(0,0)]
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