What is the complement of set of integers between zero and ten in the universal set defined by the integers from zero to 20?

Given the problem:

1. The set of integers between 0 and 10, inclusive, is:
   \[
   A = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
   \]

2. The universal set, \( U \), is the set of integers from 0 to 20, inclusive:
   \[
   U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}
   \]

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

So, the complement of \( A \) is:
\[
A^c = \{11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}
\]

Would you like further details on set operations or any related questions?

Here are some related questions:
1. What is the difference between a set's complement and its subset?
2. How would you find the complement if the universal set was different?
3. What is the intersection between two sets?
4. How can you use Venn diagrams to visualize complements?
5. How do union and intersection relate to complements in set theory?

**Tip:** The complement of a set depends entirely on the universal set, so always define the universal set clearly before finding the complement.

What is the complement of the set of integers between zero and ten in the universal set defined by the integers from zero to 20?

Discover how to find the complement of the set of integers from 0 to 10 within the universal set from 0 to 20. This set theory problem explains the complement formula and its application, suitable for students in Grades 6-8.

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