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Let's solve the problem step by step.

We are given the following sets:
- **Re (Conjunto Referencial)** = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- **A** = {2, 3, 4, 5, 6, 7}
- **B** = {5, 6, 7, 8, 9}
- **C** = {1, 2, 3, 4, 5, 9, 10}

The operation is \((A \cap B)^c - (B - C)\).

### 1. Find \(A \cap B\):
\(A \cap B\) is the intersection of sets A and B (common elements between A and B).

- A = {2, 3, 4, 5, 6, 7}
- B = {5, 6, 7, 8, 9}

Common elements = {5, 6, 7}

So, \(A \cap B = \{5, 6, 7\}\).

### 2. Find \((A \cap B)^c\):
The complement \((A \cap B)^c\) means all elements in the universal set \(Re\) that are **not** in \(A \cap B\).

- \(A \cap B = \{5, 6, 7\}\)
- \(Re = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\)

The complement \((A \cap B)^c = \{1, 2, 3, 4, 8, 9, 10\}\).

### 3. Find \(B - C\):
The operation \(B - C\) means the elements in set B that are **not** in set C.

- B = {5, 6, 7, 8, 9}
- C = {1, 2, 3, 4, 5, 9, 10}

Elements in B but not in C = {6, 7, 8}

So, \(B - C = \{6, 7, 8\}\).

### 4. Find \((A \cap B)^c - (B - C)\):
Now, subtract the set \(B - C\) from \((A \cap B)^c\).

- \((A \cap B)^c = \{1, 2, 3, 4, 8, 9, 10\}\)
- \(B - C = \{6, 7, 8\}\)

Remove the elements of \(B - C\) from \((A \cap B)^c\):

\[
(A \cap B)^c - (B - C) = \{1, 2, 3, 4, 8, 9, 10\} - \{6, 7, 8\}
\]
Result = \{1, 2, 3, 4, 9, 10\}.

### 5. The correct answer:
Looking at the options provided:
- a) {1, 2, 3, 4, 5, 6}
- b) {2, 3, 4, 5, 6, 7}
- c) {1, 2, 3, 4, 8, 9}
- d) {1, 2, 3, 4, 9, 10}

The correct answer is **d) {1, 2, 3, 4, 9, 10}**.

Would you like more details or have any questions? 

Here are 5 related questions for further practice:
1. What is the result of \((A \cup B) - C\) for the same sets?
2. How do you find the symmetric difference between two sets?
3. What is the complement of set A with respect to the universal set \(Re\)?
4. What is the intersection of \(B\) and \(C\)?
5. How do you find the union of three sets?

**Tip:** Always check if the operation involves a universal set when dealing with complements. It helps to visualize the problem clearly!

¿Cuál es el resultado de la operación (A ∩ B)^c - (B - C)? Dado Re = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 3, 4, 5, 6, 7}, B = {5, 6, 7, 8, 9}, C = {1, 2, 3, 4, 5, 9, 10}.

Find the result of the set operation (A ∩ B)^c - (B - C), using set theory concepts like complement and difference. Sets A = {2, 3, 4, 5, 6, 7}, B = {5, 6, 7, 8, 9}, C = {1, 2, 3, 4, 5, 9, 10}, and the universal set Re = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

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