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The text in the image appears to be written in Russian and involves set theory operations. It looks like you are asked to define certain set operations through other basic operations. Here is a transcription and breakdown of the problem:

1. **First line**: 
   - **Define the operation ∪ (union)** through operations `{∩ (intersection), \ (set difference)};`
2. **Second line**:
   - **Define the operation ∩ (intersection)** through operations `{∪ (union), \ (set difference)};`
3. **Third line**:
   - **Define the operation \ (set difference)** through operations `{∩ (intersection), ∪ (union)};`

### Let's break down the steps you would take to define these:

1. **Define union ( ∪ )** using intersection ( ∩ ) and set difference ( \ ):
   - The union of sets A and B can be expressed as:
     \[
     A \cup B = (A \setminus B) \cup (B \setminus A) \cup (A \cap B)
     \]

2. **Define intersection ( ∩ )** using union ( ∪ ) and set difference ( \ ):
   - The intersection of sets A and B can be written as:
     \[
     A \cap B = A \setminus (A \setminus B)
     \]

3. **Define set difference ( \ )** using intersection ( ∩ ) and union ( ∪ ):
   - The set difference of A and B is:
     \[
     A \setminus B = A \cap (U \setminus B)
     \]
   where \( U \) is the universal set (this depends on the context provided, often assumed in set theory).

Would you like further explanation on any of these operations or details about the logical structure?

Here are five questions to explore further:
1. What are the properties of the union operation in set theory?
2. How does set difference differ from symmetric difference?
3. Can De Morgan’s laws be used to redefine these operations?
4. What role does the universal set play in the definition of set operations?
5. How can we visualize set operations with Venn diagrams?

**Tip**: Understanding the relationship between union, intersection, and set difference is key to mastering set theory concepts, as they form the foundation for more complex operations like symmetric difference.

Define the set operations (union ∪, intersection ∩, and set difference \) through other operations.

Learn how to define union, intersection, and set difference using basic set operations like intersection and set difference. This set theory problem covers key mathematical concepts with detailed formulas and explanations. Suitable for advanced high school and college students.

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