Sets A and B are subsets of the universal set U. These sets are defined as follows. U= {f, k, q, r, s, x,y} A = {f.q.x} B = {f,r,y} Find the following sets.
Sets A and B are subsets of the universal set U. These sets are defined as follows. U= {f, k, q, r, s, x,y} A = {f.q.x} B = {f,r,y} Find the following sets.
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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![### Unions, Intersections, and Complements Involving 2 Sets
#### Sets \( A \) and \( B \) are subsets of the universal set \( U \).
These sets are defined as follows:
\[
U = \{ f, k, q, r, s, x, y \}
\]
\[
A = \{ f, q, x \}
\]
\[
B = \{ r, y \}
\]
#### Find the following sets. Write your answer in [roster form](https://en.wikipedia.org/wiki/Set_notation#Roster_or_tabular_form) or as \(\varnothing\).
1. **(a) \((A \cup B)'\):**
- The complement of the union of sets \( A \) and \( B \).
2. **(b) \( A' \cap B \):**
- The intersection of the complement of set \( A \) and set \( B \).
#### Additional Information:
- **Complement** (\( '\ )):
- The complement of a set \( A \), denoted by \( A' \), includes all the elements in the universal set \( U \) that are not in \( A \).
- **Union** (\( \cup \)):
- The union of two sets \( A \) and \( B \) is a set containing all elements of \( A \) and \( B \).
- **Intersection** (\( \cap \)):
- The intersection of two sets \( A \) and \( B \) is a set containing only the elements that are both in \( A \) and \( B \).
Please submit your answers in the provided input fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a4d37d3-cfd7-49ff-9170-60cb41cb998b%2F3cab8da1-44b4-4f0a-a712-8ff926da0cb8%2Fe9i78js_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Unions, Intersections, and Complements Involving 2 Sets
#### Sets \( A \) and \( B \) are subsets of the universal set \( U \).
These sets are defined as follows:
\[
U = \{ f, k, q, r, s, x, y \}
\]
\[
A = \{ f, q, x \}
\]
\[
B = \{ r, y \}
\]
#### Find the following sets. Write your answer in [roster form](https://en.wikipedia.org/wiki/Set_notation#Roster_or_tabular_form) or as \(\varnothing\).
1. **(a) \((A \cup B)'\):**
- The complement of the union of sets \( A \) and \( B \).
2. **(b) \( A' \cap B \):**
- The intersection of the complement of set \( A \) and set \( B \).
#### Additional Information:
- **Complement** (\( '\ )):
- The complement of a set \( A \), denoted by \( A' \), includes all the elements in the universal set \( U \) that are not in \( A \).
- **Union** (\( \cup \)):
- The union of two sets \( A \) and \( B \) is a set containing all elements of \( A \) and \( B \).
- **Intersection** (\( \cap \)):
- The intersection of two sets \( A \) and \( B \) is a set containing only the elements that are both in \( A \) and \( B \).
Please submit your answers in the provided input fields.
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