Which of the following is correct?

Options

A. Predecessor of successor of 1000 is 1000
B. Predecessor of predeccessor of 1000 Is 999
C. Successor of predecessor of 1000 is 1001
D. Successor of predecessor of 1000 is 1002

Answer

To solve the question, we need to analyze the statements given and determine which one is correct based on the definitions of predecessor and successor.

### Step-by-Step Solution:

1. **Understanding Predecessor and Successor:**
- **Predecessor**: The number that comes before a given number.
- **Successor**: The number that comes after a given number.

2. **Finding the Successor of 1000:**
- The successor of 1000 is calculated as:
\[ 1000 + 1 = 1001 \]

3. **Finding the Predecessor of the Successor of 1000:**
- Now, we need to find the predecessor of the successor (1001):
\[ 1001 - 1 = 1000 \]
- Thus, the predecessor of the successor of 1000 is 1000.

4. **Evaluating the First Option:**
- The first option states that the predecessor of the successor of 1000 is 1000. This is correct.

5. **Finding the Predecessor of 1000:**
- The predecessor of 1000 is:
\[ 1000 - 1 = 999 \]

6. **Finding the Predecessor of the Predecessor of 1000:**
- The predecessor of 999 is:
\[ 999 - 1 = 998 \]
- Thus, the predecessor of the predecessor of 1000 is 998.

7. **Evaluating the Second Option:**
- The second option states that the predecessor of the predecessor of 1000 is 999. This is incorrect since we found it to be 998.

8. **Finding the Predecessor of 1000 Again:**
- As previously calculated, the predecessor of 1000 is 999.

9. **Finding the Successor of the Predecessor of 1000:**
- The successor of 999 is:
\[ 999 + 1 = 1000 \]

10. **Evaluating the Third Option:**
- The third option states that the successor of the predecessor of 1000 is 1001. This is incorrect since we found it to be 1000.

11. **Finding the Successor of the Predecessor of 1000 Again:**
- We already calculated that the predecessor of 1000 is 999, and its successor is 1000.

12. **Evaluating the Fourth Option:**
- The fourth option states that the successor of the predecessor of 1000 is 1002. This is incorrect since we found it to be 1000.

### Conclusion:
- The only correct statement is the first option: **The predecessor of the successor of 1000 is 1000.**