https://file.aiquickdraw.com/mathbot/file/1726541823276k9ncalls.jpg

The problem in the image states:

Let \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \) and \( A = \{1\} \). Find the set \( A^c \).

### Solution:

- \( U \) is the universal set, and it contains all the elements: \(\{1, 2, 3, 4, 5, 6, 7, 8, 9\}\).
- \( A \) is a subset of \( U \), specifically \( A = \{1\} \).
- \( A^c \), the complement of \( A \), consists of all the elements in \( U \) that are *not* in \( A \).

Thus, to find \( A^c \), we subtract the elements of \( A \) from \( U \):
\[
A^c = U - A = \{2, 3, 4, 5, 6, 7, 8, 9\}.
\]

### Final Answer:
\[
A^c = \{2, 3, 4, 5, 6, 7, 8, 9\}.
\]

Would you like further details or clarification?

### 5 Related Questions:
1. What is the complement of a set in general set theory?
2. How do you find the union of two sets?
3. What is the intersection of sets \( A \) and \( B \) if \( A = \{1\} \) and \( B = \{3, 4\} \)?
4. Can the complement of a set ever be larger than the universal set?
5. How would you represent the complement of a set visually using a Venn diagram?

### Tip:
Always check that the union of a set and its complement equals the universal set. This ensures your complement is calculated correctly!

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1}. Find the set A^c.

Learn how to find the complement of the set A = {1} when the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. A simple set theory problem suitable for students in Grades 6-8.

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