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A = {2n | n € Z}, B = {3n | n € Z}, C = {4n | n € Z}, D = {6n | n € Z}, E = {8n | n € Z} where Z is the set of integers. Which of the following are true and which are false? a) ESCCA b) BSD c) DCB d) DC Ā

A = {2n | n € Z}, B = {3n | n € Z}, C = {4n | n € Z}, D = {6n | n € Z}, E = {8n | n € Z} where Z is the set of integers. Which of the following are true and which are false? a) ESCCA b) BSD c) DCB d) DC Ā

Database System Concepts
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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**Transcription:** Sets are defined as follows: - \( A = \{2n \mid n \in \mathbb{Z}\} \) - \( B = \{3n \mid n \in \mathbb{Z}\} \) - \( C = \{4n \mid n \in \mathbb{Z}\} \) - \( D = \{6n \mid n \in \mathbb{Z}\} \) - \( E = \{8n \mid n \in \mathbb{Z}\} \) where \(\mathbb{Z}\) is the set of integers. Determine which of the following statements are true and which are false: a) \( E \subseteq C \subseteq A \) b) \( B \subseteq D \) c) \( D \subseteq B \) d) \( \overline{D} \subseteq \overline{A} \) **Explanation:** This exercise involves identifying possible subset relations among five sets. Each set is defined using multiples of integers. Statements a), b), c), and d) test the knowledge of subset relations, where \( \subseteq \) denotes a subset. The task is to verify these relations based on the definitions of the sets \( A, B, C, D, \) and \( E \).
Transcribed Image Text:**Transcription:** Sets are defined as follows: - \( A = \{2n \mid n \in \mathbb{Z}\} \) - \( B = \{3n \mid n \in \mathbb{Z}\} \) - \( C = \{4n \mid n \in \mathbb{Z}\} \) - \( D = \{6n \mid n \in \mathbb{Z}\} \) - \( E = \{8n \mid n \in \mathbb{Z}\} \) where \(\mathbb{Z}\) is the set of integers. Determine which of the following statements are true and which are false: a) \( E \subseteq C \subseteq A \) b) \( B \subseteq D \) c) \( D \subseteq B \) d) \( \overline{D} \subseteq \overline{A} \) **Explanation:** This exercise involves identifying possible subset relations among five sets. Each set is defined using multiples of integers. Statements a), b), c), and d) test the knowledge of subset relations, where \( \subseteq \) denotes a subset. The task is to verify these relations based on the definitions of the sets \( A, B, C, D, \) and \( E \).
Expert Solution
Step 1 Solution

(a) False

Explanation :-As, E is not a subset of C and C is not a subset of A, so it is false.

(b) True

Explanation :-As, B=3n  and D=6n D can be written as D=2*3n.So, B is the subset of D

(c) False

Explanation :-As it can be seen that D is 6 n and B is 3 n so, D is not a subset of B. 

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