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Let's solve the questions step-by-step based on the image you uploaded, which contains set operations.

### Given sets:
- \( S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)
- \( A = \{1, 2, 3, 4, 5\} \)
- \( B = \{2, 3, 4, 5, 6\} \)
- \( C = \{6, 7, 8, 9\} \)

### 1. \( A \cup B \) (Union of A and B):
Union of two sets combines all elements, removing duplicates.
\[ A \cup B = \{1, 2, 3, 4, 5, 6\} \]

### 2. \( A \cup C \):
Union of \( A \) and \( C \):
\[ A \cup C = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \]

### 3. \( A \cap B \cap C \) (Intersection of A, B, and C):
Intersection includes elements common to all sets.
\[ A \cap B = \{2, 3, 4, 5\} \]
Now, intersect with \( C \):
\[ A \cap B \cap C = \emptyset \] (No elements are common in all three sets.)

### 4. \( AC - B \) (Difference between A and B's complement, denoted as \( A^c - B \)):
First, find the complement of \( A \) in \( S \), which is all elements in \( S \) but not in \( A \).
\[ A^c = S - A = \{6, 7, 8, 9, 10\} \]
Now subtract \( B \) from \( A^c \):
\[ A^c - B = \{6, 7, 8, 9, 10\} - \{2, 3, 4, 5, 6\} = \{7, 8, 9, 10\} \]

### 5. \( BC + C \) (Union of B's complement and C):
Find the complement of \( B \) in \( S \):
\[ B^c = S - B = \{1, 7, 8, 9, 10\} \]
Now, take the union of \( B^c \) and \( C \):
\[ B^c \cup C = \{1, 7, 8, 9, 10\} \cup \{6, 7, 8, 9\} = \{1, 6, 7, 8, 9, 10\} \]

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Would you like to continue with the remaining questions, or do you have any questions so far? Here are 5 related questions for further practice:

1. What is \( B \cap C \)?
2. Find \( A^c \cap C \).
3. What is \( B^c - C \)?
4. Calculate \( A \cup B^c \).
5. Determine \( (A \cap C) \cup (B \cap C) \).

**Tip**: When dealing with set operations, using a Venn diagram can help visualize unions, intersections, and complements effectively.

Diketahui beberapa himpunan berikut: S = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, B = {2,3,4,5,6}, C = {6,7,8,9}. Maka tentukanlah hasil dari: 1. A ∪ B, 2. A ∪ C, 3. A ∩ B ∩ C, 4. A^c - B, 5. B^c + C, 6. (C ∩ A)^c - B, 7. A ∩ B ∩ C^c, 8. (A ∪ B) ∪ (A ∪ C), 9. (B ∩ A) - (A ∪ B)^c, 10. (A ∪ C) + (A ∪ B)^c

Pelajari bagaimana melakukan operasi himpunan pada soal yang melibatkan A, B, C, dan S. Ini mencakup operasi union, intersection, complement, dan difference antara beberapa himpunan, cocok untuk siswa SMA kelas 10-12.

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