Let R1 be a partial order on X, and let R2 a partial order on Y. Let R be a relation on X x Y defined by: (x1, Y1) R (x2, Y2) → x1 R1 x2 ^ Yı R2 Y2- Show that R is a partial order on X × Y. Let S = {1,2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c, d) 2a – b = 2c – d. (i) Show that R is an equivalence relation. (ii) If S = {1,2, 3, 4, 5, 6, 7, 8}, find R[(2,5)], the equivalence class of (2,5).

Let R1 be a partial order on X, and let R2 a partial order on Y. Let R be a relation on X x Y defined by: (x1, Y1) R (x2, Y2) → x1 R1 x2 ^ Yı R2 Y2- Show that R is a partial order on X × Y. Let S = {1,2, 3, ...}. Let R be a relation on he set S x S defined by (a, b) R (c, d) 2a – b = 2c – d. (i) Show that R is an equivalence relation. (ii) If S = {1,2, 3, 4, 5, 6, 7, 8}, find R[(2,5)], the equivalence class of (2,5).

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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