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Hallar:
A ∪ B ∪ C =
A ∩ B ∩ C =
B Δ C =
A - C =


Let's analyze the Venn diagram and extract the necessary data to solve the problem. The numbers in the regions of the sets represent the elements that belong to specific parts of sets \( A \), \( B \), and \( C \).

### 1. \( A \cup B \cup C \) (Union of \( A \), \( B \), and \( C \))
The union of sets \( A \), \( B \), and \( C \) includes all elements in any of these sets. From the diagram, the elements in \( A \cup B \cup C \) are:
\[
\{ 1, 2, 3, 4, 5, 6, 7 \}
\]
So, \( A \cup B \cup C = \{ 1, 2, 3, 4, 5, 6, 7 \} \).

### 2. \( A \cap B \cap C \) (Intersection of \( A \), \( B \), and \( C \))
The intersection of sets \( A \), \( B \), and \( C \) includes only the elements that are common to all three sets. From the diagram, the only element in all three sets is \( 2 \).
\[
A \cap B \cap C = \{ 2 \}
\]

### 3. \( B \Delta C \) (Symmetric difference between \( B \) and \( C \))
The symmetric difference between \( B \) and \( C \) includes the elements that are in \( B \) or \( C \), but not in both. From the diagram:
- Elements in \( B \): \( \{ 2, 3, 4 \} \)
- Elements in \( C \): \( \{ 2, 5, 6, 7 \} \)
The elements that are in \( B \) or \( C \) but not both are:
\[
B \Delta C = \{ 3, 4, 5, 6, 7 \}
\]

### 4. \( A - C \) (Elements in \( A \) but not in \( C \))
This includes the elements that are in \( A \) but not in \( C \). From the diagram:
- Elements in \( A \): \( \{ 1, 2, 6, 7 \} \)
- Elements in \( C \): \( \{ 2, 5, 6, 7 \} \)
The elements that are in \( A \) but not in \( C \) are:
\[
A - C = \{ 1 \}
\]

### Summary of the Results:
- \( A \cup B \cup C = \{ 1, 2, 3, 4, 5, 6, 7 \} \)
- \( A \cap B \cap C = \{ 2 \} \)
- \( B \Delta C = \{ 3, 4, 5, 6, 7 \} \)
- \( A - C = \{ 1 \} \)

Let me know if you need further details or clarifications.

Here are some related questions for practice:
1. Find \( A \cap B \).
2. What is \( B - A \)?
3. Calculate \( (A \cup B) \cap C \).
4. What is the symmetric difference \( A \Delta B \)?
5. Find the number of elements in \( (A \cap B) \cup C \).

**Tip:** When analyzing Venn diagrams, always pay attention to which regions correspond to different set operations, such as unions, intersections, and differences.

Hallar: A ∪ B ∪ C, A ∩ B ∩ C, B Δ C, A - C

Solve the set theory problem using a Venn diagram to find the union, intersection, symmetric difference, and difference of sets A, B, and C. This guide covers core set theory concepts for students in Grades 9-12.

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