Let S be the universal set, where: S = {1,2,3,..., 28, 29, 30} Let sets A and B be subsets of S, where: Set A={14, 19, 20, 21, 22, 27, 30} Set B = {2, 11, 12, 15, 16, 26} Set C = {3,4,6,7,9, 14, 17, 26, 30} Find the number of elements in the set (An B) n(An B)=
Let S be the universal set, where: S = {1,2,3,..., 28, 29, 30} Let sets A and B be subsets of S, where: Set A={14, 19, 20, 21, 22, 27, 30} Set B = {2, 11, 12, 15, 16, 26} Set C = {3,4,6,7,9, 14, 17, 26, 30} Find the number of elements in the set (An B) n(An B)=
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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![# Venn Diagram Intersections
## Problem Statement:
Let \( S \) be the universal set, where:
\[ S = \{1, 2, 3, \ldots, 28, 29, 30\} \]
Let sets \( A \), \( B \), and \( C \) be subsets of \( S \), where:
- **Set A**: \( A = \{14, 19, 20, 21, 22, 27, 30\} \)
- **Set B**: \( B = \{2, 11, 12, 15, 16, 26\} \)
- **Set C**: \( C = \{3, 4, 6, 7, 9, 14, 17, 26, 30\} \)
## Tasks:
1. **Find the number of elements in the set \( A \cap B \)**:
\[
n(A \cap B) = \_\_\_\_
\]
2. **Find the number of elements in the set \( B \cap C \)**:
\[
n(B \cap C) = \_\_\_\_
\]
3. **Find the number of elements in the set \( A \cap C \)**:
\[
n(A \cap C) = \_\_\_\_
\]
### Optional:
You may want to draw a Venn Diagram to help answer these questions.
## Solution Steps:
1. **Find \( A \cap B \)**:
\[
A \cap B = \{14, 19, 20, 21, 22, 27, 30\} \cap \{2, 11, 12, 15, 16, 26\} = \{\}
\]
So, \( n(A \cap B) = 0 \).
2. **Find \( B \cap C \)**:
\[
B \cap C = \{2, 11, 12, 15, 16, 26\} \cap \{3, 4, 6, 7, 9, 14, 17, 26, 30\} = \{26\}
\]
So, \( n(B \cap C) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2Fe943486a-03d8-44de-8f87-b87db12aa5fa%2F9t7c3cu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Venn Diagram Intersections
## Problem Statement:
Let \( S \) be the universal set, where:
\[ S = \{1, 2, 3, \ldots, 28, 29, 30\} \]
Let sets \( A \), \( B \), and \( C \) be subsets of \( S \), where:
- **Set A**: \( A = \{14, 19, 20, 21, 22, 27, 30\} \)
- **Set B**: \( B = \{2, 11, 12, 15, 16, 26\} \)
- **Set C**: \( C = \{3, 4, 6, 7, 9, 14, 17, 26, 30\} \)
## Tasks:
1. **Find the number of elements in the set \( A \cap B \)**:
\[
n(A \cap B) = \_\_\_\_
\]
2. **Find the number of elements in the set \( B \cap C \)**:
\[
n(B \cap C) = \_\_\_\_
\]
3. **Find the number of elements in the set \( A \cap C \)**:
\[
n(A \cap C) = \_\_\_\_
\]
### Optional:
You may want to draw a Venn Diagram to help answer these questions.
## Solution Steps:
1. **Find \( A \cap B \)**:
\[
A \cap B = \{14, 19, 20, 21, 22, 27, 30\} \cap \{2, 11, 12, 15, 16, 26\} = \{\}
\]
So, \( n(A \cap B) = 0 \).
2. **Find \( B \cap C \)**:
\[
B \cap C = \{2, 11, 12, 15, 16, 26\} \cap \{3, 4, 6, 7, 9, 14, 17, 26, 30\} = \{26\}
\]
So, \( n(B \cap C) =
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