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(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that rRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If z and y are elements of B such that r + y and rSy, then (y,1) ¢ S.

(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that rRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If z and y are elements of B such that r + y and rSy, then (y,1) ¢ S.

Elements Of Modern Algebra
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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can i get some help with binary and relation true or false question

 

Let S and T be equivalence relations on a set B.

(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that xRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If x and y are elements of B such that r + y and rSy, then (y, x) 4 S.
Transcribed Image Text:(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that xRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If x and y are elements of B such that r + y and rSy, then (y, x) 4 S.
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