Problem 1. Answer the following questions. 1(a) Is this relation partial order? If yes, is it a total order? Justify your answer: The domain is a group of brothers and sisters. Ry if y is at least as old as r. You can assume that all the brothers and sisters have the same mother, so no two of them were born at exactly the same time. 1(b) Is this relation an equivalence relation? If yes, describe the partition defined by the equivalence classes. Justify your answer: The domain is the set of all integers. rEy if r + y is even. (An integer z is even if z = 2k for some integer k.)

Problem 1. Answer the following questions. 1(a) Is this relation partial order? If yes, is it a total order? Justify your answer: The domain is a group of brothers and sisters. Ry if y is at least as old as r. You can assume that all the brothers and sisters have the same mother, so no two of them were born at exactly the same time. 1(b) Is this relation an equivalence relation? If yes, describe the partition defined by the equivalence classes. Justify your answer: The domain is the set of all integers. rEy if r + y is even. (An integer z is even if z = 2k for some integer k.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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