Let U={1,2,3,...,10}, A={1,3,5,7}, B ={1,2,3,4}, and C={3,4,6,7,9). Select (AUC)n B from the choices below. {7,8} {4,5} {6,8} {8,10} {3,9} 00 Check Answer
Let U={1,2,3,...,10}, A={1,3,5,7}, B ={1,2,3,4}, and C={3,4,6,7,9). Select (AUC)n B from the choices below. {7,8} {4,5} {6,8} {8,10} {3,9} 00 Check Answer
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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![### Problem Statement:
Let \( U = \{1, 2, 3, \ldots, 10\} \), \( A = \{1, 3, 5, 7\} \), \( B = \{1, 2, 3, 4\} \), and \( C = \{3, 4, 6, 7, 9\} \).
Select \( (A \cup C)^c \cap B^c \) from the choices below.
#### Options:
- \( \{7, 8\} \)
- \( \{4, 5\} \)
- \( \{6, 8\} \)
- \( \{8, 10\} \)
- \( \{3, 9\} \)
- \( \emptyset \)
#### Explanation of the Sets:
- \( U \) (Universal set): \( \{1, 2, 3, \ldots, 10\} \)
- \( A \): \( \{1, 3, 5, 7\} \)
- \( B \): \( \{1, 2, 3, 4\} \)
- \( C \): \( \{3, 4, 6, 7, 9\} \)
### Step-by-Step Solution:
1. **Find \( A \cup C \)**:
\[
A \cup C = \{1, 3, 5, 7\} \cup \{3, 4, 6, 7, 9\} = \{1, 3, 4, 5, 6, 7, 9\}
\]
2. **Find the complement of \( A \cup C \) within the universal set \( U \)**:
\[
(A \cup C)^c = U - (A \cup C) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} - \{1, 3, 4, 5, 6, 7, 9\} = \{2, 8, 10\}
\]
3. **Find the complement of \( B \) within the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F0be91451-bb64-479a-ac1b-1e3f14076cd5%2F6xrlexl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Let \( U = \{1, 2, 3, \ldots, 10\} \), \( A = \{1, 3, 5, 7\} \), \( B = \{1, 2, 3, 4\} \), and \( C = \{3, 4, 6, 7, 9\} \).
Select \( (A \cup C)^c \cap B^c \) from the choices below.
#### Options:
- \( \{7, 8\} \)
- \( \{4, 5\} \)
- \( \{6, 8\} \)
- \( \{8, 10\} \)
- \( \{3, 9\} \)
- \( \emptyset \)
#### Explanation of the Sets:
- \( U \) (Universal set): \( \{1, 2, 3, \ldots, 10\} \)
- \( A \): \( \{1, 3, 5, 7\} \)
- \( B \): \( \{1, 2, 3, 4\} \)
- \( C \): \( \{3, 4, 6, 7, 9\} \)
### Step-by-Step Solution:
1. **Find \( A \cup C \)**:
\[
A \cup C = \{1, 3, 5, 7\} \cup \{3, 4, 6, 7, 9\} = \{1, 3, 4, 5, 6, 7, 9\}
\]
2. **Find the complement of \( A \cup C \) within the universal set \( U \)**:
\[
(A \cup C)^c = U - (A \cup C) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} - \{1, 3, 4, 5, 6, 7, 9\} = \{2, 8, 10\}
\]
3. **Find the complement of \( B \) within the
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