If $a$ and $b$ are two numbers such that $ab = 0$, then

### Concept & Rule This problem tests the **Zero Product Property** of real numbers. $$ab = 0 \implies a = 0 \text{ or } b = 0$$ ### Step-by-Step Solution * **Given:** The product of two numbers $a$ and $b$ is zero ($ab = 0$). * **Deduction:** For any multiplication to result in zero, at least one of the factors must be zero. * It is possible that $a = 0$ while $b$ is any non-zero number (e.g., $0 \times 5 = 0$). * It is possible that $b = 0$ while $a$ is any non-zero number (e.g., $7 \times 0 = 0$). * It is also possible that both are zero ($0 \times 0 = 0$). * Therefore, the condition covers $a = 0$, or $b = 0$, or both. ### Exam Strategy & Shortcut This is a direct theoretical question. Recognize the exact definition of the zero product property to immediately eliminate the options that use "and" exclusively or require one variable to be strictly non-zero. ### Common Pitfall A common mistake is selecting "$a = 0$ and $b = 0$" assuming both must be zero, or missing the "or both" condition. The mathematical "or" is inclusive, meaning it accounts for either or both. ### Final Answer Therefore, the correct answer is **$a = 0$ or $b = 0$ or both**.