Consider the following statements about natural numbers
1. There exists a smallest natural number.
2. Thre exists a largest natural number.
3. Between two natural numbers, there is always a natural number.
Which of these is/are correct?

Options

A. None
B. Only 1
C. 1 and 2
D. 2 and 3

Answer

To analyze the statements about natural numbers, let's evaluate each one step by step.

### Step 1: Evaluate the first statement
**Statement 1:** There exists a smallest natural number.

Natural numbers are defined as the set of positive integers starting from 1. Therefore, the smallest natural number is 1.

**Conclusion:** This statement is **true**.

### Step 2: Evaluate the second statement
**Statement 2:** There exists a largest natural number.

Natural numbers continue indefinitely (1, 2, 3, 4, ...). There is no largest natural number because you can always add 1 to any natural number to get another natural number.

**Conclusion:** This statement is **false**.

### Step 3: Evaluate the third statement
**Statement 3:** Between two natural numbers, there is always a natural number.

For any two natural numbers, say 1 and 2, there is no natural number between them. The natural numbers are discrete and do not include fractions or decimals. Therefore, between any two consecutive natural numbers, there are no other natural numbers.

**Conclusion:** This statement is **false**.

### Final Conclusion
Based on the evaluations:
- Statement 1 is true.
- Statement 2 is false.
- Statement 3 is false.

Thus, only the first statement is correct.

### Answer:
The correct answer is: **Only one statement is true (Statement 1)**.

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