Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
1.) A = {a, b, c, d, e, f, g, x, y, z}, B = {c, r, a, z, y}.
1a.) n(A)
1b.) n(B)
1c.) n(A ∩ B)
1d.) n(A ∪ B)
![Here is the transcription of the text from the image suitable for an educational website, including explanations for any mathematical expressions:
---
### Set Operations and Cardinality
Consider the sets \( A \) and \( B \) defined as follows:
\[ A = \{a, b, c, d, e, f, g, x, y, z\} \]
\[ B = \{c, r, a, z, y\} \]
We are to find the following:
(a) \(n(A)\)
(b) \(n(B)\)
(c) \(n(A \cap B)\)
(d) \(n(A \cup B)\)
**Explanation:**
- **(a) \(n(A)\)**: This represents the cardinality of set \(A\), which is the number of elements in set \(A\).
- **(b) \(n(B)\)**: This represents the cardinality of set \(B\), which is the number of elements in set \(B\).
- **(c) \(n(A \cap B)\)**: This represents the cardinality of the intersection of sets \(A\) and \(B\), which is the number of elements that are common to both sets.
- **(d) \(n(A \cup B)\)**: This represents the cardinality of the union of sets \(A\) and \(B\), which is the total number of distinct elements in either set.
To calculate these, follow these steps:
1. **Finding \(n(A)\)**:
List the number of distinct elements in set \(A\).
\[ A = \{a, b, c, d, e, f, g, x, y, z\} \]
**Number of elements**: 10
2. **Finding \(n(B)\)**:
List the number of distinct elements in set \(B\).
\[ B = \{c, r, a, z, y\} \]
**Number of elements**: 5
3. **Finding \(n(A \cap B)\)**:
List the elements that are common to both sets \(A\) and \(B\).
\[ A \cap B = \{a, c, y, z\} \]
**Number of common elements**: 4
4. **Finding \(n(A \cup B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff726d6fd-4af8-4bb0-826c-a6698fefcdb5%2F38c61f0d-ebee-41be-8245-315a107b541c%2F4h3l7in_processed.png&w=3840&q=75)
Transcribed Image Text:Here is the transcription of the text from the image suitable for an educational website, including explanations for any mathematical expressions:
---
### Set Operations and Cardinality
Consider the sets \( A \) and \( B \) defined as follows:
\[ A = \{a, b, c, d, e, f, g, x, y, z\} \]
\[ B = \{c, r, a, z, y\} \]
We are to find the following:
(a) \(n(A)\)
(b) \(n(B)\)
(c) \(n(A \cap B)\)
(d) \(n(A \cup B)\)
**Explanation:**
- **(a) \(n(A)\)**: This represents the cardinality of set \(A\), which is the number of elements in set \(A\).
- **(b) \(n(B)\)**: This represents the cardinality of set \(B\), which is the number of elements in set \(B\).
- **(c) \(n(A \cap B)\)**: This represents the cardinality of the intersection of sets \(A\) and \(B\), which is the number of elements that are common to both sets.
- **(d) \(n(A \cup B)\)**: This represents the cardinality of the union of sets \(A\) and \(B\), which is the total number of distinct elements in either set.
To calculate these, follow these steps:
1. **Finding \(n(A)\)**:
List the number of distinct elements in set \(A\).
\[ A = \{a, b, c, d, e, f, g, x, y, z\} \]
**Number of elements**: 10
2. **Finding \(n(B)\)**:
List the number of distinct elements in set \(B\).
\[ B = \{c, r, a, z, y\} \]
**Number of elements**: 5
3. **Finding \(n(A \cap B)\)**:
List the elements that are common to both sets \(A\) and \(B\).
\[ A \cap B = \{a, c, y, z\} \]
**Number of common elements**: 4
4. **Finding \(n(A \cup B
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education