2. For this entire page, let A = {x E Z: 6< x< 10 and 2|x} a. List the elements of A. b. List the objects in the power set of A, 24. c. Please label each of the following statements as either true or false. (You do not need to prove your assertions.) i. 10 E A 1i. 14 E A iii. {6} € A iv. Ø E A v. 8 E 24 vi. {8} € 24 vii. Ø E 24 ix. 10 CA x. {10} C A xi. A C A xii. Ø C A xiі. 10 с 24 xiv. (10} C 24 xv. {{8}, {10}} C 24 xvi. A C 24 viii. A E 24
2. For this entire page, let A = {x E Z: 6< x< 10 and 2|x} a. List the elements of A. b. List the objects in the power set of A, 24. c. Please label each of the following statements as either true or false. (You do not need to prove your assertions.) i. 10 E A 1i. 14 E A iii. {6} € A iv. Ø E A v. 8 E 24 vi. {8} € 24 vii. Ø E 24 ix. 10 CA x. {10} C A xi. A C A xii. Ø C A xiі. 10 с 24 xiv. (10} C 24 xv. {{8}, {10}} C 24 xvi. A C 24 viii. A E 24
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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Please help with question 2 in images. Thank you.
![### Problem Statement
For this entire page, let \( A = \{ x \in \mathbb{Z} : 6 \leq x \leq 10 \text{ and } 2|x \} \).
#### a. List the elements of \( A \).
Since \( A \) is the set of integers \( x \) such that \( 6 \leq x \leq 10 \) and \( x \) is even, the elements of \( A \) are:
\[ A = \{ 6, 8, 10 \} \]
#### b. List the objects in the power set of \( A \), \( 2^A \).
The power set \( 2^A \) of the set \( A = \{ 6, 8, 10 \} \) includes all possible subsets of \( A \):
\[ 2^A = \{ \emptyset, \{6\}, \{8\}, \{10\}, \{6, 8\}, \{6, 10\}, \{8, 10\}, \{6, 8, 10\} \} \]
#### c. Please label each of the following statements as either true or false. (You do not need to prove your assertions.)
**Statements:**
i. \( 10 \in A \) __________
ii. \( 14 \in A \) __________
iii. \( \{6\} \in A \) __________
iv. \( \emptyset \in A \) __________
v. \( 8 \in 2^A \) __________
vi. \( \{8\} \in 2^A \) __________
vii. \( \emptyset \in 2^A \) __________
viii. \( A \in 2^A \) __________
ix. \( 10 \subseteq A \) __________
x. \( \{10\} \subseteq A \) __________
xi. \( A \subseteq A \) __________
xii. \( \emptyset \subseteq A \) __________
xiii. \( 10 \subseteq 2^A \) __________
xiv. \( \{10\} \subseteq 2^A \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F620c60a1-10fe-416e-8b85-1e75a34b227e%2F12dfb1dd-999e-4eea-82dd-fd9fc448168e%2Fgmix4b8_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
For this entire page, let \( A = \{ x \in \mathbb{Z} : 6 \leq x \leq 10 \text{ and } 2|x \} \).
#### a. List the elements of \( A \).
Since \( A \) is the set of integers \( x \) such that \( 6 \leq x \leq 10 \) and \( x \) is even, the elements of \( A \) are:
\[ A = \{ 6, 8, 10 \} \]
#### b. List the objects in the power set of \( A \), \( 2^A \).
The power set \( 2^A \) of the set \( A = \{ 6, 8, 10 \} \) includes all possible subsets of \( A \):
\[ 2^A = \{ \emptyset, \{6\}, \{8\}, \{10\}, \{6, 8\}, \{6, 10\}, \{8, 10\}, \{6, 8, 10\} \} \]
#### c. Please label each of the following statements as either true or false. (You do not need to prove your assertions.)
**Statements:**
i. \( 10 \in A \) __________
ii. \( 14 \in A \) __________
iii. \( \{6\} \in A \) __________
iv. \( \emptyset \in A \) __________
v. \( 8 \in 2^A \) __________
vi. \( \{8\} \in 2^A \) __________
vii. \( \emptyset \in 2^A \) __________
viii. \( A \in 2^A \) __________
ix. \( 10 \subseteq A \) __________
x. \( \{10\} \subseteq A \) __________
xi. \( A \subseteq A \) __________
xii. \( \emptyset \subseteq A \) __________
xiii. \( 10 \subseteq 2^A \) __________
xiv. \( \{10\} \subseteq 2^A \
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