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 CardinalityConsider 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**: 102. **Finding $n(B)$**: List the number of distinct elements in set $B$. \[ B = \{c, r, a, z, y\} \] **Number of elements**: 53. **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**: 44. **Finding \(n(A \cup B

Answered: Image /qna-images/answer/38c61f0d-ebee-41be-8245-315a107b541c.jpg

Answered: A = {a, b, c, d, e, f, g, x, y, z), B =…

A = {a, b, c, d, e, f, g, x, y, z), B = {c, r, a, z, y}. Find the following. (See Example 1.) (a) n(A) (b) n(B) (c) n(An B) (d) n(A U B)

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,...

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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

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