"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-06 13:56:48.861898
"""

```python
from typing import List, Tuple

class FactChecker:
    """
    A simple fact-checking system that evaluates statements against a predefined set of facts.
    """

    def __init__(self, facts: List[Tuple[str, bool]]):
        """
        Initialize the fact-checker with a list of (statement, truth_value) tuples.

        :param facts: List of tuples where each tuple contains a statement and its truth value
        """
        self.facts = dict(facts)

    def check_fact(self, statement: str) -> Tuple[str, bool]:
        """
        Check if the given statement is true or false based on the predefined facts.

        :param statement: The statement to be checked
        :return: A tuple containing the statement and its truth value
        """
        return self.facts.get(statement, (statement, None))

    def add_fact(self, statement: str, truth_value: bool) -> None:
        """
        Add a new fact to the system.

        :param statement: The statement to be added as a new fact
        :param truth_value: The truth value of the new fact
        """
        self.facts[statement] = (truth_value)

    def remove_fact(self, statement: str) -> None:
        """
        Remove an existing fact from the system.

        :param statement: The statement to be removed
        """
        if statement in self.facts:
            del self.facts[statement]

def example_usage():
    # Example facts about simple statements
    initial_facts = [
        ("The sky is blue", True),
        ("Water boils at 100 degrees Celsius", True),
        ("AI can solve complex problems", False)
    ]
    
    fact_checker = FactChecker(initial_facts)

    print("Checking if 'The sky is blue' is true:", fact_checker.check_fact("The sky is blue"))
    print("Checking if 'Grass is red' is true:", fact_checker.check_fact("Grass is red"))

    # Adding a new fact
    fact_checker.add_fact("Python is a programming language", True)
    print("Adding the fact that Python is a programming language")
    
    # Removing an existing fact
    fact_checker.remove_fact("AI can solve complex problems")
    print("Removing the fact about AI solving complex problems")

if __name__ == "__main__":
    example_usage()
```

This code defines a `FactChecker` class which can be used to check the truth of statements against a predefined set of facts. It includes methods for checking if a statement is true, adding new facts, and removing existing ones. The `example_usage` function demonstrates how to use this class.