Refer to B={ ={₁0, -6, 0.23, 3, -1.7, √7}. Determine which elements belong to the given set. Separate your answers with commas, if necessary. J 0/6 8 (a) 0.3 EN (b) E W 00 T (c)-6, 3, 0,-1.7 EZ (d) E Q 23' 3 S (e) EH ,0,-6,0.₁3,-1.7, √ ER 4 8 E

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Mathematical Sets and Elements Identification**

Refer to \( B = \left\{ \frac{\pi}{3}, 0, -6, 0.23, 3, -1.7, \sqrt{7} \right\} \). Determine which elements belong to the given set. Separate your answers with commas, if necessary.

**Questions:**

(a) \( 0.3 \in \mathbb{N} \)

(b) \(  \square \in \mathbb{W} \)

(c) \( -6, 3, 0, -1.7 \in \mathbb{Z} \)

(d) \( \square, \frac{\pi}{3} \in \mathbb{Q} \)

(e) \( \square \in \mathbb{H} \)

(f) \( \frac{\pi}{3}, 0, -6, 0.23, 3, -1.7, \sqrt{7} \in \mathbb{R} \)

**Key for Symbols and Sets:**
- \( \pi \) symbol (π)
- Square root symbol (\(\sqrt{}\))
- Square box symbols intended for user inputs (⬛)
- The letter \( \mathbb{N} \) represents the set of natural numbers
- The letter \( \mathbb{W} \) represents the set of whole numbers
- The letter \( \mathbb{Z} \) represents the set of integers
- The letter \( \mathbb{Q} \) represents the set of rational numbers
- The letter \( \mathbb{H} \) represents the set of Hurwitz quaternions (elements \( \in \mathbb{H} \) must be specified)
- The letter \( \mathbb{R} \) represents the set of real numbers

**Explanation:**
- Each option has a prompt about the membership of certain numbers to particular sets.
- Some options provide specific elements to be identified directly from the set \( B \).
- The numeric inputs are to be matched with their respective sets.
Transcribed Image Text:**Mathematical Sets and Elements Identification** Refer to \( B = \left\{ \frac{\pi}{3}, 0, -6, 0.23, 3, -1.7, \sqrt{7} \right\} \). Determine which elements belong to the given set. Separate your answers with commas, if necessary. **Questions:** (a) \( 0.3 \in \mathbb{N} \) (b) \( \square \in \mathbb{W} \) (c) \( -6, 3, 0, -1.7 \in \mathbb{Z} \) (d) \( \square, \frac{\pi}{3} \in \mathbb{Q} \) (e) \( \square \in \mathbb{H} \) (f) \( \frac{\pi}{3}, 0, -6, 0.23, 3, -1.7, \sqrt{7} \in \mathbb{R} \) **Key for Symbols and Sets:** - \( \pi \) symbol (π) - Square root symbol (\(\sqrt{}\)) - Square box symbols intended for user inputs (⬛) - The letter \( \mathbb{N} \) represents the set of natural numbers - The letter \( \mathbb{W} \) represents the set of whole numbers - The letter \( \mathbb{Z} \) represents the set of integers - The letter \( \mathbb{Q} \) represents the set of rational numbers - The letter \( \mathbb{H} \) represents the set of Hurwitz quaternions (elements \( \in \mathbb{H} \) must be specified) - The letter \( \mathbb{R} \) represents the set of real numbers **Explanation:** - Each option has a prompt about the membership of certain numbers to particular sets. - Some options provide specific elements to be identified directly from the set \( B \). - The numeric inputs are to be matched with their respective sets.
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