1 Point {n E Z: 2

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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**Question: Q3.1**

**Point Value: 1 Point**

**Task:**
Write out the indicated sets by listing their elements between braces.

**Sets Description:**

1. { \( n \in \mathbb{Z} : 2 < n < 5 \) }
   - This set includes integers \( n \) such that \( 2 < n < 5 \).
   - Elements of this set are \{3, 4\}.

2. { \( n \in \mathbb{Z} : |n| = 5 \) }
   - This set includes integers \( n \) where the absolute value of \( n \) is 5.
   - Elements of this set are \{-5, 5\}.

**Requested Calculation:**

Calculate the Cartesian product of these sets:

- \(\{3, 4\} \times \{-5, 5\}\)

The Cartesian product results in ordered pairs combining each element of the first set with each element of the second set. 

**Resulting Cartesian Product:**
\[
\{ (3, -5), (3, 5), (4, -5), (4, 5) \}
\]
Transcribed Image Text:**Question: Q3.1** **Point Value: 1 Point** **Task:** Write out the indicated sets by listing their elements between braces. **Sets Description:** 1. { \( n \in \mathbb{Z} : 2 < n < 5 \) } - This set includes integers \( n \) such that \( 2 < n < 5 \). - Elements of this set are \{3, 4\}. 2. { \( n \in \mathbb{Z} : |n| = 5 \) } - This set includes integers \( n \) where the absolute value of \( n \) is 5. - Elements of this set are \{-5, 5\}. **Requested Calculation:** Calculate the Cartesian product of these sets: - \(\{3, 4\} \times \{-5, 5\}\) The Cartesian product results in ordered pairs combining each element of the first set with each element of the second set. **Resulting Cartesian Product:** \[ \{ (3, -5), (3, 5), (4, -5), (4, 5) \} \]
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