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We are given the following sets:

- \( A = [-6; 1] \) 
- \( B = (-4; 2) \) 
- \( C = (-6; -4) \)

The task is to determine which statement is **false**.

Let's go through the options one by one.

### 1. \((A \cap B) \setminus C = (-4; 1]\)

- First, find the intersection \( A \cap B \):
  - \( A = [-6; 1] \) and \( B = (-4; 2) \).
  - The intersection would be the range where both sets overlap, which is \( (-4; 1] \).

- Now, calculate \((A \cap B) \setminus C\):
  - \( C = (-6; -4) \).
  - Subtract \( C \) from \( (-4; 1] \). Since \( C = (-6; -4) \) does not overlap with \( (-4; 1] \), this operation doesn't affect the set.
  - So, the result is still \( (-4; 1] \).

Thus, the first statement is **true**.

### 2. \((A \cup B) \setminus C = (-4; 2)\)

- First, calculate the union \( A \cup B \):
  - \( A = [-6; 1] \) and \( B = (-4; 2) \), so \( A \cup B = [-6; 2) \).

- Now, compute \((A \cup B) \setminus C\):
  - Subtract \( C = (-6; -4) \) from \( [-6; 2) \).
  - This gives \( (-4; 2) \).

Thus, the second statement is **true**.

### 3. \( A \cup B \cup C = [-6; 2)\)

- \( A \cup B \cup C = [-6; 2) \), as the union of \( A = [-6; 1] \), \( B = (-4; 2) \), and \( C = (-6; -4) \) results in \( [-6; 2) \).

Thus, the third statement is **true**.

### 4. \( A \cap B \cap C = \emptyset \)

- Find the intersection \( A \cap B \cap C \):
  - \( A = [-6; 1] \), \( B = (-4; 2) \), and \( C = (-6; -4) \).
  - \( A \cap B = (-4; 1] \).
  - \( (-4; 1] \cap C = (-4; -4] \), which is an empty set.

Thus, the fourth statement is **true**.

### 5. \((A \cap B) \setminus C = (-4; 2)\)

- From the earlier calculation, we found that \((A \cap B) \setminus C = (-4; 1]\), not \( (-4; 2) \).

Thus, the fifth statement is **false**.

### Conclusion:
The **false** statement is the fifth one: \((A \cap B) \setminus C = (-4; 2)\).

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Would you like any further explanation or details on any of these steps?

Here are 5 related questions:
1. What is the difference between set union and set intersection?
2. How do you find the complement of a set?
3. How does set subtraction work?
4. Can a union of sets be smaller than the original sets?
5. What happens if two sets have no overlap?

**Tip:** Always double-check the boundaries when performing set operations to avoid small errors.

Cho ba tập hợp A = [-6; 1], B = (-4; 2), C = (-6; -4). Khẳng định nào sau đây sai?

Explore a set theory problem involving union, intersection, and difference of sets. The question asks to find which of the given statements is false based on the sets A = [-6; 1], B = (-4; 2), and C = (-6; -4). Includes detailed explanations of each step and correct solutions.

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