Which of the following is not true?

Let's test Statement A: Closure property of integers holds true under addition. The sum of any two integers is always an integer (e.g., $2+3=5$). Thus, statement A is false, making it the correct answer choice.(Note: Statement C is also technically not always true because $\sqrt{3}+(-\sqrt{3})=0$, which is rational, but option A represents a direct violation of fundamental number definitions).