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}

Given that the universal set \( U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \), we are tasked with finding the complement of the set \( A = \{ x \mid x \in \mathbb{N}, x < 7 \} \).

### Step 1: Define Set \( A \)
The set \( A \) is defined as the natural numbers \( x \) such that \( x < 7 \) and belongs to the universal set \( U \). So, the set \( A \) is:
\[
A = \{0, 1, 2, 3, 4, 5, 6\}
\]

### Step 2: Find the Complement of \( A \)
The complement of a set \( A \), denoted \( A^c \), consists of all elements in the universal set \( U \) that are not in \( A \). Therefore, we subtract the elements of \( A \) from \( U \):
\[
A^c = U - A = \{7, 8, 9, 10\}
\]

### Final Answer:
The complement of the set \( A \) is:
\[
\{7, 8, 9, 10\}
\]

Would you like further explanation or have any questions?

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**Related questions:**
1. What is the complement of a set with respect to a different universal set?
2. How does set complement work in infinite sets?
3. How can set complements be applied in probability?
4. What is the relationship between the union of a set and its complement?
5. How does De Morgan’s law apply to complements of sets?

**Tip:** When finding the complement, always ensure you know the elements in the universal set to avoid errors.

Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x | x is in N and x < 7}

Learn how to find the complement of the set {x | x is in N and x < 7} from the universal set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. This problem covers key set theory concepts, including finding complements of sets. Suitable for students in Grades 6-8.

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