U​ = { 4​, 5​, 6​, 7​, 8​, 9​, 10 ​}, A​ = { 5​, 6​, 9​, 10 ​} set A

Given the universal set \( U = \{ 4, 5, 6, 7, 8, 9, 10 \} \) and the subset \( A = \{ 5, 6, 9, 10 \} \), let's explore the properties of set \( A \) within the context of \( U \).

### Analysis of Set \( A \):
1. **Elements of Set \( A \)**: The set \( A \) consists of the elements 5, 6, 9, and 10.
2. **Subset Relationship**: Since all elements of \( A \) are also in \( U \), \( A \) is a subset of \( U \), denoted as \( A \subseteq U \).
3. **Complement of \( A \)**: The complement of \( A \) in \( U \), denoted as \( A' \) or \( U \setminus A \), is the set of elements in \( U \) that are not in \( A \). So,
   \[
   A' = \{ 4, 7, 8 \}
   \]
4. **Cardinality of \( A \)**: The number of elements in \( A \) is \( |A| = 4 \).
5. **Cardinality of \( U \)**: The number of elements in \( U \) is \( |U| = 7 \).

Would you like further details on this analysis or have any specific questions? 

### Relative Questions:
1. What is the union of sets \( A \) and \( A' \)?
2. How do you find the intersection of sets \( A \) and \( A' \)?
3. What is the cardinality of the complement of set \( A \)?
4. Can you list all possible subsets of set \( A \)?
5. How would you represent set \( A \) in terms of a Venn diagram?

### Tip:
When dealing with sets, always ensure you clearly define the universal set \( U \) as it provides the context for operations like complements and unions.

Explore the properties of subset A within the universal set U. Learn about subsets, complements, and cardinality in set theory with a detailed analysis. Suitable for students in Grades 7-9.

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