Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A:G = IAU{(a,b), (b, a), (b, c) , (c, b), (a, c), (c, a), (d, e) , (e, d) , (g, h), (h, g)},H = IAU{(b, c) , (c, b), (g, h), (h, g)} .6.Clearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H, (A/H)/(G/H).

Given that A = a , b , c , d , e , f , g , h . Also, G and H are the following equivalence…

Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G = IAU{(a,b) , (b, a), (b, c) , (c, b) , (a, c) , (c, a) , (d, e) , (e, d) , (g, h) , (h, g)}, H = IAU{(b, c) , (c, b) , (g, h) , (h, g)}. Clearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H, (A/H){(G/H).

Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G = IAU{(a,b) , (b, a), (b, c) , (c, b) , (a, c) , (c, a) , (d, e) , (e, d) , (g, h) , (h, g)}, H = IAU{(b, c) , (c, b) , (g, h) , (h, g)}. Clearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H, (A/H){(G/H).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...

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