Find the complement of the set given that
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(Enter your answers as a comma-separated list.)
{x | x is in N and x < 7}

To find the complement of a set, we need to subtract the given set from the universal set \( U \). The universal set is:

\[
U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\]

The set given is:
\[
A = \{x \mid x \text{ is in } \mathbb{N} \text{ and } x < 7\}
\]
So, the set \( A \) contains:
\[
A = \{0, 1, 2, 3, 4, 5, 6\}
\]

To find the complement of \( A \) (denoted as \( A^c \)), we subtract \( A \) from \( U \), which gives us the elements that are in \( U \) but not in \( A \):
\[
A^c = U - A = \{7, 8, 9, 10\}
\]

So, the complement of the set is:
\[
A^c = \{7, 8, 9, 10\}
\]

### Do you need further clarification or details?

Here are 5 related questions:
1. What is the definition of the complement of a set?
2. How would you find the complement if the universal set were infinite?
3. What is the union of a set and its complement?
4. How would you represent the complement using Venn diagrams?
5. How does the complement change if the universal set changes?

**Tip**: The complement of a set always contains elements from the universal set that are not in the original set.

Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list.) {x | x is in N and x < 7}

Learn how to find the complement of a set within a given universal set. This example uses the universal set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and finds the complement of the set {x | x is in N and x < 7}. Suitable for students in Grades 6-8.

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