https://file.aiquickdraw.com/mathbot/file/17259772814174v0mhjrj.jpg

Let's go through the set operations outlined in your image. The sets provided are:

- \( A = \{1, 3, 5, 6, 7, 8, 9\} \)
- \( B = \{2, 4, 6, 8, 10\} \)
- \( C = \{3, 6, 9\} \)
- \( D = \{4, 8\} \)

I'll evaluate each of the expressions step by step. Let's start from the top and go down the list:

### 1. \( A \cup B \) (Union of A and B)
Union includes all distinct elements from both sets:
\[
A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\]

### 2. \( B \cap C \) (Intersection of B and C)
Intersection includes only the elements common in both sets:
\[
B \cap C = \{6\}
\]

### 3. \( C \cup D \) (Union of C and D)
\[
C \cup D = \{3, 4, 6, 8, 9\}
\]

### 4. \( B \cup D \) (Union of B and D)
\[
B \cup D = \{2, 4, 6, 8, 10\}
\]

### 5. \( A - B \) (Difference: Elements in A but not in B)
\[
A - B = \{1, 3, 5, 7, 9\}
\]

### 6. \( A - C \) (Difference: Elements in A but not in C)
\[
A - C = \{1, 5, 7, 8\}
\]

### 7. \( A - D^c \) (Elements in A minus the complement of D)
First, find \( D^c \), the complement of \( D \) relative to the universal set (assuming the universal set to be \( A \cup B \cup C \cup D \)):
\[
D^c = \{1, 2, 3, 5, 6, 7, 9, 10\}
\]
Now, \( A - D^c \) would result in:
\[
A - D^c = \{8\}
\]

### 8. \( C^c - C \) (Complement of C minus C)
Find \( C^c \), the complement of C:
\[
C^c = \{1, 2, 4, 5, 7, 8, 10\}
\]
Now, \( C^c - C \):
\[
C^c - C = \{1, 2, 4, 5, 7, 8, 10\}
\]

### 9. \( D^c - B \) (Complement of D minus B)
We already found \( D^c = \{1, 2, 3, 5, 6, 7, 9, 10\} \).
Now subtract \( B \) from \( D^c \):
\[
D^c - B = \{1, 3, 5, 7, 9\}
\]

### 10. \( (C \cup D) \cap B \)
Find the union of \( C \) and \( D \):
\[
C \cup D = \{3, 4, 6, 8, 9\}
\]
Now intersect with \( B \):
\[
(C \cup D) \cap B = \{4, 6, 8\}
\]

---

I have completed the first 10 operations. Would you like me to continue solving the rest of the expressions (11-20), or would you like to ask specific questions about these operations?

Here are five related questions to further explore:

1. How is the complement of a set determined in a given universal set?
2. What happens when you take the union of disjoint sets?
3. How does the order of operations affect complex set operations?
4. What role do set complements play in real-life applications of set theory?
5. How can Venn diagrams be used to visualize the operations between sets?

**Tip:** In set theory, understanding the difference between union and intersection is key, as union collects all elements while intersection narrows down to shared elements.

Perform set operations such as union, intersection, difference, and complement on sets A, B, C, and D. Evaluate the expressions provided step by step.

Explore step-by-step solutions for performing set operations, including union, intersection, difference, and complement, on sets A = {1, 3, 5, 6, 7, 8, 9}, B = {2, 4, 6, 8, 10}, C = {3, 6, 9}, and D = {4, 8}. Suitable for students in Grades 10-12.

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