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It looks like you've uploaded an image with a series of set theory exercises. I’ll help you solve the first few exercises. Let’s start with **Ejercicio 11**, which involves finding the union \( A \cup B \).

### Ejercicio 11: Hallar la unión \( A \cup B \)

1. **Caso 1:**
   - \( A = \{ x \in \mathbb{Z} \ | \ -2 \leq x \leq 5 \} = \{-2, -1, 0, 1, 2, 3, 4, 5\} \)
   - \( B = \{ x \in \mathbb{Z} \ | \ -5 \leq x \leq 3 \} = \{-5, -4, -3, -2, -1, 0, 1, 2, 3\} \)

   The union is:
   \[
   A \cup B = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}
   \]

2. **Caso 2:**
   - \( A = \{ x \in \mathbb{N} \ | \ 1 \leq x \leq 8 \} = \{1, 2, 3, 4, 5, 6, 7, 8\} \)
   - \( B = \{ x \in \mathbb{N} \ | \ 6 \leq x \leq 12 \} = \{6, 7, 8, 9, 10, 11, 12\} \)

   The union is:
   \[
   A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
   \]

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### Ejercicio 12: Hallar la intersección \( A \cap B \)

1. **Caso 1:**
   - \( A = \{ x \in \mathbb{R} \ | \ 0 \leq x \leq 5 \} \)
   - \( B = \{ y \in \mathbb{R} \ | \ 0 \leq y \leq 10 \} \)

   The intersection is:
   \[
   A \cap B = \{x \in \mathbb{R} \ | \ 0 \leq x \leq 5\}
   \]

2. **Caso 2:**
   - \( A = \{ x \in \mathbb{R} \ | -1 < x \leq 1/4 \} \)
   - \( B = \{ z \in \mathbb{R} \ | -1 < z < 0 \lor 0 < z \leq 3 \} \)

   The intersection is:
   \[
   A \cap B = \{x \in \mathbb{R} \ | -1 < x < 0\}
   \]

---

Would you like to continue with the next exercises or any further details? Let me know if you have any questions!

### 5 Related Questions:
1. How is the complement of a set defined relative to a universal set?
2. What is the difference between union and intersection in set theory?
3. How would you represent the union of three sets, \( A \cup B \cup C \)?
4. What is a symmetric difference between two sets?
5. How do the properties of intersection change when dealing with subsets?

### Tip:
Always visualize set operations like union and intersection using Venn diagrams to better understand their relationships.

Solve exercises involving union, intersection, complements, and differences in set theory.

Solve exercises related to union, intersection, and complements of sets with step-by-step solutions. Understand core concepts like union (A ∪ B), intersection (A ∩ B), and set complement. Suitable for high school students.

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