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The image contains two problems related to set theory. Here is a breakdown of each:

### Problem 27:
You are given the following system of set equations:
\[
\begin{cases}
A \cap X = B, \\
A \cup X = C,
\end{cases}
\]
where \( A \), \( B \), and \( C \) are given sets, and it's specified that \( B \subseteq A \subseteq C \).

### Solution to Problem 27:
1. From the first equation \( A \cap X = B \), this means that the intersection of \( A \) and \( X \) must equal \( B \), which implies that every element of \( B \) is in both \( A \) and \( X \), and no other elements of \( A \) are in \( X \) except those in \( B \).

2. From the second equation \( A \cup X = C \), we know that the union of \( A \) and \( X \) must equal \( C \). This implies that \( X \) must contain all elements of \( C \) that are not in \( A \), plus potentially some elements from \( A \).

Given that \( B \subseteq A \subseteq C \), we can determine \( X \) as:
- \( X = B \cup (C \setminus A) \)

Thus, the solution to Problem 27 is:
\[
X = B \cup (C \setminus A)
\]

### Problem 28:
You are given a new system of set equations:
\[
\begin{cases}
A \setminus X = B, \\
X \setminus A = C,
\end{cases}
\]
where \( A \), \( B \), and \( C \) are given sets, and \( B \subseteq A \), with \( A \cap C = \emptyset \).

### Solution to Problem 28:
1. From the first equation \( A \setminus X = B \), this means that the elements in \( A \) but not in \( X \) must be equal to \( B \). Therefore, \( X \) contains all the elements of \( A \setminus B \).

2. From the second equation \( X \setminus A = C \), we see that the elements in \( X \) but not in \( A \) must equal \( C \). Thus, \( X \) also contains all the elements of \( C \).

Given the condition \( A \cap C = \emptyset \), we know that \( C \) and \( A \) have no elements in common.

Therefore, \( X \) is:
\[
X = (A \setminus B) \cup C
\]

### Final Answer for Problem 28:
\[
X = (A \setminus B) \cup C
\]

---

Would you like further clarification or more detailed explanations? Here are some related questions to deepen your understanding:

1. What does the notation \( A \cap X = B \) imply about the relationship between sets \( A \), \( B \), and \( X \)?
2. How does \( A \cup X = C \) help in determining the elements of \( X \)?
3. What is the significance of the condition \( B \subseteq A \subseteq C \) in set theory?
4. Why is it important that \( A \cap C = \emptyset \) in Problem 28?
5. Can you find a practical example where such set equations might be useful?

**Tip:** In set theory, breaking down the equations into basic operations like union, intersection, and difference helps in visualizing the structure of the solution.

Решить систему уравнений: 1) A ∩ X = B, A ∪ X = C; 2) A \ X = B, X \ A = C, где A, B и C — данные множества и B ⊆ A ⊆ C.

Explore how to solve a system of set equations involving union, intersection, and set difference. This solution covers concepts like A ∩ X = B and A ∪ X = C, with conditions B ⊆ A ⊆ C. Suitable for advanced high school or university-level students studying set theory.

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