please show the correct answer and steps (13) # Set Theory Practice ProblemsIn the following problems, we are given a universal set \( U \) and three subsets \( A \), \( B \), and \( C \) of \( U \). We will work on finding elements for specific set operations.## Given Sets**Universal set \( U \)**:\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17\} \]**Subsets**:- \( A = \{3, 4, 5, 9, 15, 16\} \)- \( B = \{1, 4, 7, 9, 10, 11, 17\} \)- \( C = \{4, 8, 13, 14, 17\} \)## Problems & Solutions### 1. List the elements in the set \( B^c \cup \emptyset \)\[ B^c \cup \emptyset = \{ \} \]Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.### 2. List the elements in the set \( A \cap B \)\[ A \cap B = \{ \} \]Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.### 3. List the elements in the set \( B^c \cup C \)\[ B^c \cup C = \{ \} \]Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.### 4. List the elements in the set \( (A \cap C) \cap B^c \)\[ (A \cap C) \cap B^c = \{ \} \]Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.*You may want to draw a Venn Diagram to help answer this question.*

We have to find given sets using given data.Concept/formula required:1)2)3)4)5)

Let U be the universal set, where: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17} Let sets A, B, and C be subsets of U, where: A = {3, 4, 5, 9, 15, 16} B = {1, 4, 7, 9, 10, 11, 17} C = {4, 8, 13, 14, 17} Find the following: LIST the elements in the set BU: BU0 = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set An B: An B={ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set BUC: BUC = {

Let U be the universal set, where: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17} Let sets A, B, and C be subsets of U, where: A = {3, 4, 5, 9, 15, 16} B = {1, 4, 7, 9, 10, 11, 17} C = {4, 8, 13, 14, 17} Find the following: LIST the elements in the set BU: BU0 = { } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set An B: An B={ } Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set BUC: BUC = {

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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please show the correct answer and steps (13)

# Set Theory Practice Problems

In the following problems, we are given a universal set \( U \) and three subsets \( A \), \( B \), and \( C \) of \( U \). We will work on finding elements for specific set operations.

## Given Sets
**Universal set \( U \)**:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17\} \]

**Subsets**:
- \( A = \{3, 4, 5, 9, 15, 16\} \)
- \( B = \{1, 4, 7, 9, 10, 11, 17\} \)
- \( C = \{4, 8, 13, 14, 17\} \)

## Problems & Solutions

### 1. List the elements in the set \( B^c \cup \emptyset \)
\[ B^c \cup \emptyset = \{ \} \]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

### 2. List the elements in the set \( A \cap B \)
\[ A \cap B = \{ \} \]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

### 3. List the elements in the set \( B^c \cup C \)
\[ B^c \cup C = \{ \} \]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

### 4. List the elements in the set \( (A \cap C) \cap B^c \)
\[ (A \cap C) \cap B^c = \{ \} \]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE.

*You may want to draw a Venn Diagram to help answer this question.*

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