Suppose R, S are equivalence relations on set A. Prove or disprove that (a) R-¹nS is also an equivalence relation on A; (b) RoS is also an equivalence relation on A. ((Hint: Not symmetric. An example. Let A = {a,b,c) and S = {(a, a), (b, b), (c, c), (a, b), (b, a)} and S= {(a, a), (b, b), (c, c), (b, c), (c, b)}. Then RoS={(a, a), (b, b), (c, c), (a, b), (b, a), (c, b), (a, c), (b, c), (c, b)} does not contain (c, a).

Suppose R, S are equivalence relations on set A. Prove or disprove that (a) R-¹nS is also an equivalence relation on A; (b) RoS is also an equivalence relation on A. ((Hint: Not symmetric. An example. Let A = {a,b,c) and S = {(a, a), (b, b), (c, c), (a, b), (b, a)} and S= {(a, a), (b, b), (c, c), (b, c), (c, b)}. Then RoS={(a, a), (b, b), (c, c), (a, b), (b, a), (c, b), (a, c), (b, c), (c, b)} does not contain (c, a).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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