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The image describes a question about set theory, specifically the union and intersection of relations \( R_1 \) and \( R_2 \). It asks which statement regarding the union operation is correct.

Here are the options:

- **a.** \( (R_1 \cup R_2) \cup R_1 = R_2 \)
- **b.** \( R_1 \cup (R_1 \cap R_2) = R_1 \)
- **c.** \( R_1 \cup R_2 = R_1 - R_2 \)
- **d.** \( R_1 \cup (R_1 \cap R_2) = R_2 \)
- **e.** \( R_1 \cup R_2 = R_1 \cap R_2 \)

### Explanation of Key Operations:
1. **Union (\( \cup \))**: Combines elements from both sets/relations.
2. **Intersection (\( \cap \))**: Includes only elements present in both sets/relations.
3. **Set Difference (\( - \))**: Removes elements of one set from another.

### Analyzing the Options:
- **Option a:** Incorrect. \( (R_1 \cup R_2) \cup R_1 \) would result in \( R_1 \cup R_2 \), not \( R_2 \).
- **Option b:** Correct. The union of a set with its intersection with another set results in the original set, i.e., \( R_1 \cup (R_1 \cap R_2) = R_1 \).
- **Option c:** Incorrect. Union and set difference do not equal each other in this context.
- **Option d:** Incorrect. Similar reasoning as in option b, but with the wrong result.
- **Option e:** Incorrect. Union and intersection are not equal unless the sets are identical.

### Conclusion:
The correct answer is **b**.

Would you like further explanation or details on this?

Here are 5 related questions to expand on this topic:
1. How does the set union operation differ from set intersection?
2. Can the union of two sets ever equal the intersection of those sets? Under what conditions?
3. How does the complement of a set relate to the union and intersection operations?
4. What is the distributive property of sets with respect to union and intersection?
5. How do Venn diagrams visually represent union, intersection, and set difference?

**Tip:** When working with set theory, it's helpful to draw Venn diagrams to visualize operations like union and intersection.

Operasi gabungan dari relasi R1 dan R2 dinyatakan oleh R1 ∪ R2, berarti bahwa relasi tersebut terdiri dari semua anggota yang ada di R1 atau di R2, atau di keduanya. Pernyataan yang benar mengenai kesamaan operasi union adalah...

Understand how to solve set theory problems involving union and intersection operations, specifically for relations R1 and R2. This problem covers key concepts like set union, intersection, and set difference.

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