Two different natural numbers are such that, their product is less than their sum. Then one of the number must be

Options

A. 3
B. 1
C. 2
D. 0

Answer

To solve the problem, we need to find two different natural numbers \( x \) and \( y \) such that their product is less than their sum. We will go through the steps systematically.

### Step-by-Step Solution:

1. **Define the Natural Numbers**:
Let the two different natural numbers be \( x \) and \( y \).

2. **Set Up the Inequality**:
According to the problem, we have the condition:
\[ xy < x + y \]

3. **Rearrange the Inequality**:
We can rearrange the inequality to:
\[ xy - x - y < 0 \]
This can be rewritten as:
\[ xy - x - y + 1 < 1 \]
Which simplifies to:
\[ (x - 1)(y - 1) < 1 \]

4. **Analyze the Product**:
Since \( x \) and \( y \) are natural numbers, \( x - 1 \) and \( y - 1 \) are non-negative integers. The product \( (x - 1)(y - 1) < 1 \) implies that the only possible values for \( (x - 1) \) and \( (y - 1) \) are 0.

5. **Determine Possible Values**:
If \( (x - 1) = 0 \), then \( x = 1 \). If \( (y - 1) = 0 \), then \( y = 1 \). Since \( x \) and \( y \) must be different natural numbers, one of them must be 1.

6. **Conclusion**:
Therefore, one of the numbers must be 1.

### Final Answer:
One of the numbers must be equal to 1.

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