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Check Product Evenness

Write a Python function `is_product_even(arr)` that determines whether the product of all numbers in a given list is even. The function should return `True` if the product is even, and `False` otherwise.

#### Example Usage
```python [main.nopy]
print(is_product_even([1, 2, 3]))  # Output: True
print(is_product_even([1, 1, 1]))  # Output: False
print(is_product_even([2, 4, 6]))  # Output: True
```

#### Constraints
- The input list will contain integers.
- The list can be empty, in which case the function should return `False` (as there are no numbers to multiply).
def is_product_even(arr):
    """
    Determine if the product of all numbers in the list is even.

    Args:
        arr (list): A list of integers.

    Returns:
        bool: True if the product is even, False otherwise.
    """
    # Placeholder for the solution
    pass