https://file.aiquickdraw.com/mathbot/file/17274448028472z7pjfmv.jpg

The problem you're working on asks to find the complement of the following sets. 

Here’s the information from the image:
- **Universal set (U)**: \(\{-10, -9, -8, \ldots, -1, 0, 1, 2, \ldots, 9, 10\}\), which includes integers from \(-10\) to \(10\).
- **Set A**: \(\{0, 1, 2, 3, 4, 5\}\)
- **Set X**: \(\{1, 2, 3, 4, 5, 7, 8, 9\}\)

### To find the complement of these sets:
1. **Complement of A (\(A^c\))**:
   This is the set of elements in \(U\) but not in \(A\). So, we take all the elements in \(U\) and subtract the elements in \(A\).
   \[
   A^c = U \setminus A = \{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 6, 7, 8, 9, 10\}
   \]

2. **Complement of X (\(X^c\))**:
   This is the set of elements in \(U\) but not in \(X\).
   \[
   X^c = U \setminus X = \{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 6, 10\}
   \]

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### Related Questions:
1. What are some properties of the complement in set theory?
2. How can we use Venn diagrams to visualize complements of sets?
3. How do union and intersection of complements work mathematically?
4. What is the complement of a universal set?
5. How do we apply De Morgan’s laws using complements?

**Tip:** The complement of a set always relates to the universal set it's defined within. Ensure the universal set is clear before calculating complements.

Find the complement of the following sets. Given the universal set U and sets A and X, calculate their complements.

Learn how to find the complement of sets A = {0, 1, 2, 3, 4, 5} and X = {1, 2, 3, 4, 5, 7, 8, 9} within the universal set U = {-10, -9, ..., 10}. This exercise demonstrates the concept of set complement using set theory and Venn diagrams. Suitable for Grades 9-10.

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