"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 02:35:40.731377
"""

```python
from typing import List
from functools import lru_cache


class FactChecker:
    """
    A simple fact-checking system that evaluates statements based on provided data.
    
    This class allows for checking if a statement is true or false using a predefined set of facts and rules.
    """

    def __init__(self, facts: dict):
        self.facts = facts

    @lru_cache(maxsize=None)
    def check_statement(self, statement: str) -> bool:
        """
        Check the truth value of a given statement based on the provided facts.

        :param statement: A string representing the statement to be checked.
        :return: True if the statement is true according to the facts, False otherwise.
        """
        # Placeholder for complex logic
        return any(statement in fact for fact in self.facts.values())

    def add_facts(self, new_facts: dict):
        """
        Add new facts to the system.

        :param new_facts: A dictionary where keys are statements and values are their truthfulness.
        """
        self.facts.update(new_facts)


# Example usage
if __name__ == "__main__":
    # Sample data
    sample_data = {
        "2 + 2": True,
        "3 * 4": True,
        "9 - 10": False
    }

    fact_checker = FactChecker(sample_data)
    
    print(fact_checker.check_statement("2 + 2"))  # Expected: True
    print(fact_checker.check_statement("3 * 4"))  # Expected: True
    print(fact_checker.check_statement("9 - 10"))  # Expected: False

    fact_checker.add_facts({"5 / 2": False})
    print(fact_checker.check_statement("5 / 2"))  # Expected: False
```