Find the complement of the set given that U = \{0, 1, 2, 3, 4, 5, 6, 7, 8\} 
The set of odd counting numbers less than 8

Given the universal set \( U = \{0, 1, 2, 3, 4, 5, 6, 7, 8\} \) and the set of odd counting numbers less than 8, we can first identify the set of odd counting numbers less than 8.

The odd counting numbers less than 8 are: \( A = \{1, 3, 5, 7\} \).

The complement of set \( A \) with respect to the universal set \( U \), denoted by \( A^c \), is the set of elements in \( U \) that are not in \( A \).

So, the complement \( A^c \) is:

\[
A^c = U \setminus A = \{0, 2, 4, 6, 8\}
\]

### Summary:
- **Universal Set**: \( U = \{0, 1, 2, 3, 4, 5, 6, 7, 8\} \)
- **Set \( A \)**: \( A = \{1, 3, 5, 7\} \)
- **Complement of \( A \)**: \( A^c = \{0, 2, 4, 6, 8\} \)

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Here are 5 related questions to further explore the concept:
1. How would you find the complement of a set if the universal set contains letters instead of numbers?
2. What is the union of set \( A \) and its complement \( A^c \)?
3. How do you determine the intersection of a set and its complement?
4. Can a set and its complement have any elements in common? Why or why not?
5. How does the complement of a set change if the universal set is altered?

**Tip:** Remember, the complement of a set includes all elements of the universal set that are not in the original set.

Learn how to find the complement of a set in set theory with a detailed explanation and examples. This problem involves identifying the complement of a set within a given universal set, covering fundamental concepts of set theory. Suitable for students in Grades 7-9.

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