1. Use set-roster notation to indicate the elements in the following set: S= {n € Z | -3 < n< 1}
1. Use set-roster notation to indicate the elements in the following set: S= {n € Z | -3 < n< 1}
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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![### Educational Content on Set Theory and Relations
#### 1. Set-Roster Notation
Use set-roster notation to indicate the elements in the following set:
\[ S = \{ n \in \mathbb{Z} \mid -3 < n < 1\} \]
#### 2. Visualizing with a Number Line
Use a number line to visualize the following set:
\[ S = \{ n \in \mathbb{R} \mid 5 < n < 10\} \]
#### 3. Cardinality of a Set
Let \( A = \{1, 2, 3\} \). What is \( |A| \)?
#### 4. Cardinality of a Set with Repetition
Let \( B = \{1, 2, 3, 4, 3, 2, 1\} \). What is \( |B| \)?
#### 5. Cartesian Product
Let \( A = \{1, 2, 3\} \) and \( C = \{a, b, c, d, e\} \). What is \( |A \times C| \)?
#### 6. Set-Roster Notation for Cartesian Product
Let \( A = \{1, 2\} \) and \( C = \{a, b\} \). Use set-roster notation to indicate the members of \( A \times C \).
#### 7. Relation Visualization
Let \( A = \{0, 1, 2\} \) and \( B = \{1, 2, 3\} \). If an element \( x \) in \( A \) is related to an element \( y \) in \( B \) if and only if \( x > y \), which elements \( x \) and \( y \) are related to each other?
Stated another way: \( \{ (x, y) \in A \times B \mid x > y \} \).
**Diagram Explanation:**
Visualize this relation using an arrow diagram, where arrows point from elements in set \( A \) to elements in set \( B \) if \( x > y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7094ef7-1652-40c4-b996-cb8ef3d4a300%2F236e45f5-741c-4d6f-9f7e-fe1e7c1f3751%2F21w7eu7_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content on Set Theory and Relations
#### 1. Set-Roster Notation
Use set-roster notation to indicate the elements in the following set:
\[ S = \{ n \in \mathbb{Z} \mid -3 < n < 1\} \]
#### 2. Visualizing with a Number Line
Use a number line to visualize the following set:
\[ S = \{ n \in \mathbb{R} \mid 5 < n < 10\} \]
#### 3. Cardinality of a Set
Let \( A = \{1, 2, 3\} \). What is \( |A| \)?
#### 4. Cardinality of a Set with Repetition
Let \( B = \{1, 2, 3, 4, 3, 2, 1\} \). What is \( |B| \)?
#### 5. Cartesian Product
Let \( A = \{1, 2, 3\} \) and \( C = \{a, b, c, d, e\} \). What is \( |A \times C| \)?
#### 6. Set-Roster Notation for Cartesian Product
Let \( A = \{1, 2\} \) and \( C = \{a, b\} \). Use set-roster notation to indicate the members of \( A \times C \).
#### 7. Relation Visualization
Let \( A = \{0, 1, 2\} \) and \( B = \{1, 2, 3\} \). If an element \( x \) in \( A \) is related to an element \( y \) in \( B \) if and only if \( x > y \), which elements \( x \) and \( y \) are related to each other?
Stated another way: \( \{ (x, y) \in A \times B \mid x > y \} \).
**Diagram Explanation:**
Visualize this relation using an arrow diagram, where arrows point from elements in set \( A \) to elements in set \( B \) if \( x > y \).
Transcribed Image Text:**8.** For each of the following named sets, please give an example of a member of the set and an example of something that is **not** a member of the set:
A. \( \mathbb{Z}^+ \)
i. Example member:
ii. Example of something that is **not** a member of \( \mathbb{Z}^+ \), but **is** a member of \( \mathbb{Z} \):
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