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 $A$: $A^c = \{0, 2, 4, 6, 8\}$

Would you like more details or have any questions?

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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.