For any [x] EZ/n and any kEZ, we can define k[x] by k[x] = [x] + [x] + ... + [x] k times where the result is an element of Z/n. We say k[x] is a multiple of [x]. (a) List all the multiples of [3] in Z/9. (Select all that apply.) [0] [1] [2] [3] [4] [5] ☐ [6] [7] [8] (b) List all the multiples of [3] in Z/8. (Select all that apply.) ☐ [0] □ [1] [2] [3] [4] [5] [6] [7]

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
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For any \([x] \in \mathbb{Z}/n\) and any \(k \in \mathbb{Z}\), we can define \(k[x]\) by

\[ k[x] = [x] + [x] + \cdots + [x] \]

\(k\) times

where the result is an element of \(\mathbb{Z}/n\). We say \(k[x]\) is a multiple of \([x]\).

(a) List all the multiples of \([3]\) in \(\mathbb{Z}/9\). (Select all that apply.)
- [ ] [0]
- [ ] [1]
- [ ] [2]
- [ ] [3]
- [ ] [4]
- [ ] [5]
- [ ] [6]
- [ ] [7]
- [ ] [8]

(b) List all the multiples of \([3]\) in \(\mathbb{Z}/8\). (Select all that apply.)
- [ ] [0]
- [ ] [1]
- [ ] [2]
- [ ] [3]
- [ ] [4]
- [ ] [5]
- [ ] [6]
- [ ] [7]
Transcribed Image Text:For any \([x] \in \mathbb{Z}/n\) and any \(k \in \mathbb{Z}\), we can define \(k[x]\) by \[ k[x] = [x] + [x] + \cdots + [x] \] \(k\) times where the result is an element of \(\mathbb{Z}/n\). We say \(k[x]\) is a multiple of \([x]\). (a) List all the multiples of \([3]\) in \(\mathbb{Z}/9\). (Select all that apply.) - [ ] [0] - [ ] [1] - [ ] [2] - [ ] [3] - [ ] [4] - [ ] [5] - [ ] [6] - [ ] [7] - [ ] [8] (b) List all the multiples of \([3]\) in \(\mathbb{Z}/8\). (Select all that apply.) - [ ] [0] - [ ] [1] - [ ] [2] - [ ] [3] - [ ] [4] - [ ] [5] - [ ] [6] - [ ] [7]
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