If the integers $d,a,b$ satisfy $d\mid a$ and $d\mid b$, which of the following must be true?

Step 1 (Divisibility Definition): Since $d\mid a$ and $d\mid b$, there exist integers $k_1$ and $k_2$ such that:

Step 2 (Sum the equations): We compute $a+b$:

Since $k_1,k_2$ are integers, their sum $k_1+k_2$ is also an integer. Therefore, by definition of divisibility, $d$ must divide $a+b$:

Step 3 (Conclusion): The statement $d\mid (a+b)$ is always true. This is at option index 0.