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The problem provided involves set operations, specifically the union of two sets. Let's break it down:

### Given sets:
- \( A = \{x \mid -1 \leq x < 3 \} \) (This means \(x\) is between \(-1\) and \(3\), including \(-1\) but not including 3).
- \( B = \{x \mid 2 < x \leq 5 \} \) (This means \(x\) is between \(2\) and \(5\), including \(5\) but not including \(2\)).

### Operation:
We are asked to find the union of sets \( A \) and \( B \), which is written as \( A \cup B \). The union of two sets includes all elements that are in either set.

### Step-by-step process:
1. **Set A:** 
   \[ A = \{x \mid -1 \leq x < 3 \} \]
   This includes all values from \(-1\) to just below \(3\).

2. **Set B:** 
   \[ B = \{x \mid 2 < x \leq 5 \} \]
   This includes all values from just above \(2\) to \(5\).

3. **Union of A and B:**
   To take the union, we combine both sets. Therefore, the union will include:
   - All values from \(-1\) to \(3\) from set \(A\), but we need to check where \(A\) and \(B\) overlap.
   - From \(A\), \(x\) approaches \(3\) but does not include it. From \(B\), \(x\) starts just above \(2\), so the overlap happens between \(2\) and \(3\).
   - Therefore, the union spans from \(-1\) to \(5\), including \(-1\) and \(5\).

   The correct expression for the union would be:
   \[
   A \cup B = \{ x \mid -1 \leq x \leq 5 \}
   \]

### Answer:
The correct choice is **D**, which is \( \{x \mid -1 \leq x \leq 5\} \).

Would you like more details on any specific step, or have any questions? 

Here are five related questions:
1. What is the difference between the union and the intersection of sets?
2. How do we handle open and closed intervals when performing union operations?
3. What would the intersection of sets \(A\) and \(B\) be in this case?
4. How would the result change if the inequalities in the sets were strict (i.e., \(<\) instead of \( \leq \))?
5. How does set notation translate to graphical representations like number lines?

**Tip:** When solving set operations, it's helpful to draw the intervals on a number line to visualize the union or intersection easily.

已知集合A = {x | -1 ≤ x < 3}, B = {x | 2 < x ≤ 5}, 则A ∪ B = ( )

Understand how to find the union of two sets A and B, given their intervals. The solution involves analyzing the intervals and combining them to form the union of sets. Suitable for students in Grades 7-9.

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