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Let's break down the problem step by step:

You are given a universal set \( S = \{ 1, 2, 3, \dots, 15 \} \), and two subsets:

- \( A = \{ x \mid x \text{ is a prime number between 5 and 15} \} \)
- \( B = \{ x \mid x \text{ is an odd number between 5 and 15} \} \)

### Step 1: Define the sets \( A \) and \( B \)

#### Set \( A \) (Prime numbers between 5 and 15):
Prime numbers between 5 and 15 are: \( 5, 7, 11, 13 \).

So, \( A = \{ 5, 7, 11, 13 \} \).

#### Set \( B \) (Odd numbers between 5 and 15):
Odd numbers between 5 and 15 are: \( 5, 7, 9, 11, 13, 15 \).

So, \( B = \{ 5, 7, 9, 11, 13, 15 \} \).

### Step 2: Perform the set operations

#### (a) \( A \cup B \) (Union of \( A \) and \( B \)):
The union of two sets includes all elements that are in either \( A \) or \( B \).

\[
A \cup B = \{ 5, 7, 9, 11, 13, 15 \}
\]

#### (b) \( A \cap B \) (Intersection of \( A \) and \( B \)):
The intersection of two sets includes all elements that are in both \( A \) and \( B \).

\[
A \cap B = \{ 5, 7, 11, 13 \}
\]

#### (c) \( B^c \) (Complement of \( B \) with respect to \( S \)):
The complement of \( B \) includes all elements in \( S \) that are not in \( B \).

\[
B^c = S - B = \{ 1, 2, 3, 4, 6, 8, 10, 12, 14 \}
\]

#### (d) \( A - B \) (Difference of \( A \) and \( B \)):
The difference of \( A \) and \( B \) includes all elements that are in \( A \) but not in \( B \).

\[
A - B = \emptyset \quad (\text{since all elements of } A \text{ are also in } B)
\]

### Summary of results:
- (a) \( A \cup B = \{ 5, 7, 9, 11, 13, 15 \} \)
- (b) \( A \cap B = \{ 5, 7, 11, 13 \} \)
- (c) \( B^c = \{ 1, 2, 3, 4, 6, 8, 10, 12, 14 \} \)
- (d) \( A - B = \emptyset \)

Let me know if you'd like further explanation or have any additional questions!

Here are five related questions you can try:
1. What is \( A^c \), the complement of \( A \)?
2. What is \( S - A \), the difference of \( S \) and \( A \)?
3. What is \( A \cup A^c \) in relation to the universal set \( S \)?
4. Can a prime number ever be an even number?
5. What is the symmetric difference between sets \( A \) and \( B \)?

**Tip:** When working with set operations, always ensure you fully understand the definitions of union, intersection, and difference, as they are fundamental to solving problems involving sets.

Diketahui S = {1, 2, ..., 15}. A = {x | x adalah bilangan prima antara 5 dan 15} B = {x | x adalah bilangan ganjil antara 5 dan 15} Tentukan: a. A ∪ B b. A ∩ B c. B^c d. A - B

Learn how to perform set operations such as union, intersection, complement, and difference with sets A and B, where A contains prime numbers and B contains odd numbers between 5 and 15. This exercise covers key set theory concepts and is suitable for students in Grades 9-10.

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