For a modulus n > 1, consider the relation on Z where two integers x and y are considered kn for some integer k, in which case we will write x = y(_mod_n) related whenever * - y = Select all that apply: This relation is reflexive since every integer is related to itself. This relation is symmetric since if x is related to y then y is related to x. This relation is transitive since if x is related to y and y related to z then x is related to z This relation is an equivalence relation because it is reflexive, symmetric, and transitive. This relation forms a partition of the integers into n equivalence classes. Each equivalence class contains related elements, each pair of which differs by a multiple of n Each class can be represented by one of the possible remainders when dividing an integer by n. We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

For a modulus n > 1, consider the relation on Z where two integers x and y are considered kn for some integer k, in which case we will write x = y(_mod_n) related whenever * - y = Select all that apply: This relation is reflexive since every integer is related to itself. This relation is symmetric since if x is related to y then y is related to x. This relation is transitive since if x is related to y and y related to z then x is related to z This relation is an equivalence relation because it is reflexive, symmetric, and transitive. This relation forms a partition of the integers into n equivalence classes. Each equivalence class contains related elements, each pair of which differs by a multiple of n Each class can be represented by one of the possible remainders when dividing an integer by n. We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

For a modulus n > 1, consider the relation on Z where two integers x and y are considered
related whenever x y = kn for some integer k, in which case we will write x = y( mod n)
Select all that apply:
This relation is reflexive since every integer is related to itself.
This relation is symmetric since if x is related to y then y is related to x.
This relation is transitive since if x is related to y and y related to z then x is related to z
This relation is an equivalence relation because it is reflexive, symmetric, and transitive.
This relation forms a partition of the integers into n equivalence classes.
Each equivalence class contains related elements, each pair of which differs by a multiple of n
Each class can be represented by one of the possible remainders when dividing an integer by n.
We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

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