Which of the following statements is not true?

Options

A. Every whole number has a successor.
B. Every whole number has a predecessor.
C. O is the least whole number.
D. Every natural number is a whole number.

Answer

To determine which of the following statements is not true, we need to analyze each statement one by one based on the definitions of whole numbers and natural numbers.

1. **Statement 1**: Every whole number is a successor.
- **Analysis**: A successor of a number is the number that comes right after it. For example, the successor of 0 is 1, the successor of 1 is 2, and so on. This statement is true because every whole number has a successor.

2. **Statement 2**: Every whole number has a predecessor.
- **Analysis**: A predecessor of a number is the number that comes right before it. For example, the predecessor of 1 is 0, the predecessor of 2 is 1, and so on. However, the whole number 0 does not have a predecessor in the set of whole numbers because there is no whole number less than 0. Therefore, this statement is not true.

3. **Statement 3**: 0 is the least whole number.
- **Analysis**: Whole numbers start from 0 and go on to positive infinity (0, 1, 2, 3, ...). Hence, 0 is indeed the least whole number. This statement is true.

4. **Statement 4**: Every natural number is a whole number.
- **Analysis**: Natural numbers start from 1 (1, 2, 3, ...), and all natural numbers are included in whole numbers. Therefore, this statement is true.

**Conclusion**: The statement that is not true is **"Every whole number has a predecessor."**