State whether each of the following statements is true or false. Then give an explanation, proof orcounter example to justify your answer.(i) The equivalence class [b] determined by b e B is a non-empty set(ii) If x and y are elements of B such that xRy, then [x] = [y].(iii) The distinct equivalence classes of S form a partition of B.(iv) S is a partial order relation.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3TFE: True or False Label each of the following statements as either true or false. If is an equivalence...

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