Find (AUB) U ={1,2,3,... 10} A ={1,2,3} B ={4,5,6} 

To find \((A \cup B) \cup \{1,2,3,\ldots,10\}\), we need to follow these steps:

1. **Determine \(A \cup B\)**:
   - \(A = \{1, 2, 3\}\)
   - \(B = \{4, 5, 6\}\)
   - \(A \cup B\) is the union of sets \(A\) and \(B\), which includes all elements in \(A\) and \(B\) without repetition.

\[
A \cup B = \{1, 2, 3, 4, 5, 6\}
\]

2. **Determine \((A \cup B) \cup \{1, 2, 3, \ldots, 10\}\)**:
   - We have \(A \cup B = \{1, 2, 3, 4, 5, 6\}\)
   - We also have the set \(\{1, 2, 3, \ldots, 10\}\)

\[
(A \cup B) \cup \{1, 2, 3, \ldots, 10\} = \{1, 2, 3, 4, 5, 6\} \cup \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\]

3. Combine all unique elements from both sets:
\[
(A \cup B) \cup \{1, 2, 3, \ldots, 10\} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\]

Thus, \((A \cup B) \cup \{1, 2, 3, \ldots, 10\} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\).

Do you want any details or have any questions about the solution? Here are some related questions you might find interesting:

1. What is the intersection of sets \(A\) and \(B\)?
2. How do you find the complement of a set?
3. What is the difference between the union and intersection of sets?
4. How would you represent these sets using a Venn diagram?
5. What is the result of \(A \cup (B \cup \{7, 8\})\)?
6. How do you prove that the union of sets is associative?
7. What is the symmetric difference between sets \(A\) and \(B\)?
8. How do you find the power set of \(A\)?

**Tip**: When dealing with sets, always remember that the union of sets includes all distinct elements from both sets without repetition.

Learn how to find the union of sets A and B with the set {1, 2, 3, ..., 10}. This problem covers basic set theory concepts including the union of sets. Suitable for students in Grades 7-9.

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