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Let's break down the question to find the required sets and solve the problem.

### Given:
- \( A = \{x \mid 2 < x \leq 10, x \in \text{bilangan asli} \} \)
    - \( A \) contains natural numbers greater than 2 and less than or equal to 10.
    - So, \( A = \{3, 4, 5, 6, 7, 8, 9, 10\} \).

- \( B = \{x \mid x \leq 10, x \in \text{bilangan genap} \} \)
    - \( B \) contains even numbers less than or equal to 10.
    - So, \( B = \{2, 4, 6, 8, 10\} \).

- \( C = \{x \mid 2 \leq x \leq 15, x \in \text{bilangan prima} \} \)
    - \( C \) contains prime numbers between 2 and 15.
    - So, \( C = \{2, 3, 5, 7, 11, 13\} \).

Now, let's solve the sub-questions:

#### a. Members of \( A \), \( B \), and \( C \)
- We already determined:
  - \( A = \{3, 4, 5, 6, 7, 8, 9, 10\} \)
  - \( B = \{2, 4, 6, 8, 10\} \)
  - \( C = \{2, 3, 5, 7, 11, 13\} \)

#### b. \( A \cup B \) and \( n(A \cup B) \)
- \( A \cup B \) is the union of sets \( A \) and \( B \).
  - \( A \cup B = \{2, 3, 4, 5, 6, 7, 8, 9, 10\} \)
  - \( n(A \cup B) = 9 \) (the number of elements in \( A \cup B \)).

#### c. \( A \cup C \) and \( n(A \cup C) \)
- \( A \cup C \) is the union of sets \( A \) and \( C \).
  - \( A \cup C = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13\} \)
  - \( n(A \cup C) = 11 \) (the number of elements in \( A \cup C \)).

#### d. \( B \cup C \) and \( n(B \cup C) \)
- \( B \cup C \) is the union of sets \( B \) and \( C \).
  - \( B \cup C = \{2, 3, 4, 5, 6, 7, 8, 10, 11, 13\} \)
  - \( n(B \cup C) = 10 \) (the number of elements in \( B \cup C \)).

#### e. \( A \cup B \cup C \) and \( n(A \cup B \cup C) \)
- \( A \cup B \cup C \) is the union of sets \( A \), \( B \), and \( C \).
  - \( A \cup B \cup C = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13\} \)
  - \( n(A \cup B \cup C) = 11 \) (the number of elements in \( A \cup B \cup C \)).

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Would you like further details or explanations on any part of this solution?

Here are 5 related questions to deepen your understanding:
1. How would the solution change if \( B \) included all odd numbers instead of even?
2. What is the intersection of sets \( A \cap C \)?
3. Can you find \( A \setminus C \)? What does this set represent?
4. How would you represent the union and intersection of more than three sets?
5. What if the upper limit of set \( C \) were changed to 20? How would that affect \( A \cup C \)?

**Tip:** Understanding set operations like union, intersection, and difference is key when solving problems involving multiple sets.

Diketahui:
A = {x | 2 < x ≤ 10, x ∈ bilangan asli}
B = {x | x ≤ 10, x ∈ bilangan genap}
C = {x | 2 ≤ x ≤ 15, x ∈ bilangan prima}
Tentukan anggota dari:
  a. A, B, dan C
  b. A ∪ B dan n(A ∪ B)
  c. A ∪ C dan n(A ∪ C)
  d. B ∪ C dan n(B ∪ C)
  e. A ∪ B ∪ C dan n(A ∪ B ∪ C)

Solve the set theory problem involving sets of natural numbers, even numbers, and prime numbers within a given range. This problem covers key concepts such as the union of sets, set cardinality, and prime numbers. Suitable for students in Grades 10-11.

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