MyOpenMath Suppose that U is the set defined as U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. - Find the sets A and B defined as follows. A = {x EU | x>4 and x>6} = { B = {x EU | x>4 or x>6} = { } } 6/11/23,
MyOpenMath Suppose that U is the set defined as U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. - Find the sets A and B defined as follows. A = {x EU | x>4 and x>6} = { B = {x EU | x>4 or x>6} = { } } 6/11/23,
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
Just question at the top, not number 9.
![### Understanding Sets and Set Operations
#### Problem Statement
Suppose that \( U \) is the set defined as \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \).
Find the sets \( A \) and \( B \) defined as follows:
\[ A = \{x \in U \mid x > 4 \text{ and } x > 6\} = \{ \} \]
\[ B = \{x \in U \mid x > 4 \text{ or } x > 6\} = \{ \} \]
#### Question 9
Sets \( A \) and \( B \) are both subsets of \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \) and defined as follows:
\[ A = \{x \in U : x < 9\} \]
\[ B = \{x \in U : x > 4\} \]
Find \( A \cap B \) and \( A \cup B \). Present your answer by listing the elements of the sets.
\[ A \cap B = \{ \hspace{3cm} \} \]
\[ A \cup B = \{ \hspace{3cm} \} \]
#### Explanation of Set Operations
**Intersection (\( A \cap B \))**: The intersection of two sets \( A \) and \( B \) includes all elements that are both in \( A \) and in \( B \).
**Union (\( A \cup B \))**: The union of two sets \( A \) and \( B \) includes all elements that are in \( A \), in \( B \), or in both.
### Step-by-Step Solution
1. **Identifying Elements in \( A \) and \( B \) from \( U \)**
- For set \( A \):
\[ A = \{ x \in U \mid x < 9 \} \]
So, \( A = \{ 1, 2, 3, 4, 5, 6, 7, 8 \} \)
- For set \( B \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F1abe1c78-4fca-4475-9c1e-a6dcaba90be2%2F3oe9guo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Sets and Set Operations
#### Problem Statement
Suppose that \( U \) is the set defined as \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \).
Find the sets \( A \) and \( B \) defined as follows:
\[ A = \{x \in U \mid x > 4 \text{ and } x > 6\} = \{ \} \]
\[ B = \{x \in U \mid x > 4 \text{ or } x > 6\} = \{ \} \]
#### Question 9
Sets \( A \) and \( B \) are both subsets of \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \) and defined as follows:
\[ A = \{x \in U : x < 9\} \]
\[ B = \{x \in U : x > 4\} \]
Find \( A \cap B \) and \( A \cup B \). Present your answer by listing the elements of the sets.
\[ A \cap B = \{ \hspace{3cm} \} \]
\[ A \cup B = \{ \hspace{3cm} \} \]
#### Explanation of Set Operations
**Intersection (\( A \cap B \))**: The intersection of two sets \( A \) and \( B \) includes all elements that are both in \( A \) and in \( B \).
**Union (\( A \cup B \))**: The union of two sets \( A \) and \( B \) includes all elements that are in \( A \), in \( B \), or in both.
### Step-by-Step Solution
1. **Identifying Elements in \( A \) and \( B \) from \( U \)**
- For set \( A \):
\[ A = \{ x \in U \mid x < 9 \} \]
So, \( A = \{ 1, 2, 3, 4, 5, 6, 7, 8 \} \)
- For set \( B \):
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