A=xeR/x>1, B=xeR/-2<x<3, C=xeR/2<x<5
a) AUB-C

To solve \( A \cup B - C \), we need to carefully analyze the given sets and their relationships.

### Given Sets
- \( A = \{ x \in \mathbb{R} \mid x > 1 \} \)
- \( B = \{ x \in \mathbb{R} \mid -2 < x < 3 \} \)
- \( C = \{ x \in \mathbb{R} \mid 2 < x < 5 \} \)

### Step-by-Step Solution

1. **Determine \( A \cup B \)**:
   - \( A = (1, \infty) \)
   - \( B = (-2, 3) \)
   - Union of \( A \) and \( B \), \( A \cup B \):
     \[
     A \cup B = (-2, \infty)
     \]

2. **Subtract \( C \) from \( A \cup B \)**:
   - \( C = (2, 5) \)
   - To find \( A \cup B - C \), we remove the interval \( C \) from \( A \cup B \):
     \[
     A \cup B - C = (-2, 2] \cup [5, \infty)
     \]

### Result
The set \( A \cup B - C \) is:
\[
(-2, 2] \cup [5, \infty)
\]

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How do we find the intersection of two sets?
2. What is the difference between union and intersection of sets?
3. Can you illustrate the union of two sets on a number line?
4. How do you subtract one set from another?
5. What are the basic properties of real number intervals?
6. How can Venn diagrams help in understanding set operations?
7. What are open and closed intervals in the context of real numbers?
8. How do you determine if a number belongs to a given set?

**Tip**: When dealing with set operations, visual aids like number lines and Venn diagrams can greatly enhance your understanding and help avoid mistakes.

Learn how to solve the set operation A union B minus C with a detailed step-by-step solution. This problem covers key concepts in set theory and interval notation, focusing on union and subtraction operations. Suitable for high school students.

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