The problem provided can be translated as follows:

Problem:
Prove that in a group of $n$ people, there exist two individuals $A$ and $B$ such that, among the remaining $n-2$ people, there are at least $\left\lfloor \frac{n}{2} \right\rfloor - 1$ people who either know both $A$ and $B$, or do not know either $A$ or $B$.

Interpretation:

• We are dealing with a group of $n$ people.
• The goal is to find two people, $A$ and $B$, such that among the remaining $n-2$ people, there is a certain number of individuals who have a specific relationship with $A$ and $B$.
• Specifically, there should be at least $\left\lfloor \frac{n}{2} \right\rfloor - 1$ people among the remaining $n-2$ who either know both $A$ and $B$, or do not know either of them.

This appears to be a combinatorial or graph theory problem, where relationships between people (e.g., knowing each other) are modeled as edges between vertices in a graph.

Would you like a detailed step-by-step proof of this, or further breakdown of any specific part?

Here are some related questions to deepen your understanding:

1. How is this problem related to graph theory?
2. What role does the floor function $\left\lfloor \cdot \right\rfloor$ play in this context?
3. How would the solution change for different values of $n$?
4. Could this be approached through induction? Why or why not?
5. How does the concept of mutual acquaintances impact the solution?

Tip: When dealing with problems involving social relationships, try visualizing the people as nodes in a graph and relationships as edges. This makes it easier to analyze.