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The problem you've provided is a set theory problem involving the following sets:

- **U** (the universal set) = {1, 2, 3, 4, 5, 6, 7, 8, 9}
- **A** (odd numbers less than 10) = {1, 3, 5, 7, 9}
- **B** = {2, 4, 5, 6, 8}
- **C** = {3, 6, 7, 9}

### Questions
The questions involve operations like union ( ∪ ), intersection ( ∩ ), difference ( − ), and complement (denoted by superscript c, e.g., \( A^c \)).

Let's break down some of these questions and calculate the answers.

### a. \( A - B \)
This means the elements in \( A \) that are not in \( B \).

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

So, \( A - B \) = {1, 3, 7, 9} (remove 5 since it's in \( B \)).

### b. \( A \cap B \)
This means the intersection of sets \( A \) and \( B \), which are the common elements between \( A \) and \( B \).

- \( A \cap B \) = {5} (the only common element).

### c. \( A^c \)
This is the complement of \( A \) with respect to the universal set \( U \). It contains elements in \( U \) that are not in \( A \).

- \( U \) = {1, 2, 3, 4, 5, 6, 7, 8, 9}
- \( A \) = {1, 3, 5, 7, 9}

Thus, \( A^c \) = {2, 4, 6, 8} (all even numbers).

### d. \( A \cap B^c \)
This means the intersection of \( A \) with the complement of \( B \) (elements in \( U \) but not in \( B \)).

- \( B^c \) = {1, 3, 7, 9} (elements in \( U \) but not in \( B \))
- \( A \) = {1, 3, 5, 7, 9}

Thus, \( A \cap B^c \) = {1, 3, 7, 9}.

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Would you like me to continue with the remaining operations or provide any clarifications?

### Related questions:

1. What is the result of \( B - A \)?
2. Can you calculate \( B^c \cap C \)?
3. How do we calculate \( A \cup B \)?
4. What is the result of \( A \cap C \)?
5. What is \( (A \cap B) \cup (A \cap C) \)?

#### Tip: 
For set complements, always remember that \( A^c = U - A \), meaning all elements in the universal set \( U \) that are not in \( A \).

Set theory problem involving operations on sets A, B, C, and U.

Explore set theory with operations on sets A, B, C, and the universal set U. Learn how to calculate union, intersection, difference, and complement in set operations. Suitable for students in Grades 9-11.

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