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Exercises Remember to practice good mathematics as you work Also, you should copy the problem if you are turning it in to be graded and'or read Answers for exercises cast in bold can be found in back of the book I. Let U= (1, 2,3,4.5.6, 7, 8,9, 10) and now let A= {xeUlx is even). B-(reU4 divides x).C={xeU]ifx]8, then x is even), D-{xe Ux22) an %3D )Express cach of these sets, A, B.C. D and E using the roster method Eind all possible proper subset and set equality relations among these sets

Exercises Remember to practice good mathematics as you work Also, you should copy the problem if you are turning it in to be graded and'or read Answers for exercises cast in bold can be found in back of the book I. Let U= (1, 2,3,4.5.6, 7, 8,9, 10) and now let A= {xeUlx is even). B-(reU4 divides x).C={xeU]ifx]8, then x is even), D-{xe Ux22) an %3D )Express cach of these sets, A, B.C. D and E using the roster method Eind all possible proper subset and set equality relations among these sets

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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--- ### Exercises Remember to practice good mathematics as you work on these problems. Also, you should copy the problem if you are turning it in to be graded and/or read. Answers for exercises cast in **bold** can be found in back of the book. 1. Let \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \) and now let \( A = \{ x \in U \mid x \text{ is even} \} \), \( B = \{ x \in U \mid 4 \text{ divides } x \} \), \( C = \{ x \in U \mid x|8, \text{ then } x \text{ is even} \} \), \( D = \{ x \in U \mid x \geq 2 \} \) and \( E = \{ x \in U \mid \left\lfloor \frac{x}{2} \right\rfloor \} \). a) Express each of these sets, \( A \), \( B \), \( C \), \( D \), and \( E \), using the roster method. b) Find all possible proper subset and set equality relations among these sets. --- In item 1, the problem provides a universal set \( U \) and five subsets \( A \), \( B \), \( C \), \( D \), and \( E \). The task is to express these sets explicitly by listing their elements (roster method) and then to examine the relationships between them. Explanation of Notations and Set Builder Descriptions: - **Universal Set \( U \)**: The collection of all elements under consideration, here it is \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \). - **Set \( A \)**: Composed of elements from \( U \) that are even numbers. - **Set \( B \)**: Composed of elements from \( U \) that are divisible by 4. - **Set \( C \)**: Composed of elements from \( U \) that are divisors of 8 and are also even. - **Set \( D \)**: Composed of elements
Transcribed Image Text:--- ### Exercises Remember to practice good mathematics as you work on these problems. Also, you should copy the problem if you are turning it in to be graded and/or read. Answers for exercises cast in **bold** can be found in back of the book. 1. Let \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \) and now let \( A = \{ x \in U \mid x \text{ is even} \} \), \( B = \{ x \in U \mid 4 \text{ divides } x \} \), \( C = \{ x \in U \mid x|8, \text{ then } x \text{ is even} \} \), \( D = \{ x \in U \mid x \geq 2 \} \) and \( E = \{ x \in U \mid \left\lfloor \frac{x}{2} \right\rfloor \} \). a) Express each of these sets, \( A \), \( B \), \( C \), \( D \), and \( E \), using the roster method. b) Find all possible proper subset and set equality relations among these sets. --- In item 1, the problem provides a universal set \( U \) and five subsets \( A \), \( B \), \( C \), \( D \), and \( E \). The task is to express these sets explicitly by listing their elements (roster method) and then to examine the relationships between them. Explanation of Notations and Set Builder Descriptions: - **Universal Set \( U \)**: The collection of all elements under consideration, here it is \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \). - **Set \( A \)**: Composed of elements from \( U \) that are even numbers. - **Set \( B \)**: Composed of elements from \( U \) that are divisible by 4. - **Set \( C \)**: Composed of elements from \( U \) that are divisors of 8 and are also even. - **Set \( D \)**: Composed of elements
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