For a non-zero integer a which of the following is not defined?

Options

A. `a-:0`
B. `0-:a`
C. `a-:1`
D. `1-:a`

Answer

To solve the question, "For a non-zero integer a, which of the following is not defined?", we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Options**: We have four options to evaluate:
- Option 1: \( \frac{a}{0} \)
- Option 2: \( \frac{0}{a} \)
- Option 3: \( \frac{a}{1} \)
- Option 4: \( \frac{1}{a} \)

2. **Evaluating Option 1**:
- For \( \frac{a}{0} \): Division by zero is undefined in mathematics. Therefore, this option is **not defined**.

3. **Evaluating Option 2**:
- For \( \frac{0}{a} \): Here, we are dividing zero by a non-zero integer \( a \). The result is \( 0 \). Thus, this option is **defined**.

4. **Evaluating Option 3**:
- For \( \frac{a}{1} \): Dividing any integer by 1 gives the integer itself. Therefore, this option is **defined** and equals \( a \).

5. **Evaluating Option 4**:
- For \( \frac{1}{a} \): Dividing 1 by a non-zero integer \( a \) is also defined, and the result is \( \frac{1}{a} \).

6. **Conclusion**: After evaluating all options, we find that only **Option 1** \( \frac{a}{0} \) is **not defined**.

### Final Answer:
The option that is not defined is **Option 1: \( \frac{a}{0} \)**.

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