If x and y are positive real numbers then which the following is CORRECT?

Options

A. `x gt yimplies-xgt-y`
B. `xgtyimplies-xlt-y`
C. `xgty=1/xgt1/y`
D. `xgtyimplies1/xlt(-1)/y`

Answer

To solve the question, we need to analyze the given information and options based on the properties of inequalities and the fact that \( x \) and \( y \) are positive real numbers.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that \( x \) and \( y \) are positive real numbers. This means:
\[ x > 0 \quad \text{and} \quad y > 0 \]

2. **Analyzing the Inequality**:
We are given that \( x > y \). This means that \( x \) is greater than \( y \).

3. **Multiplying by -1**:
If we multiply both sides of the inequality \( x > y \) by -1, we need to remember that multiplying or dividing an inequality by a negative number reverses the direction of the inequality. Therefore:
\[ -x < -y \]

4. **Conclusion**:
From the above step, we conclude that if \( x > y \), then it follows that \( -x < -y \). This means that the inequality holds true when we multiply by -1, but the relationship is reversed.

5. **Identifying the Correct Option**:
We need to look for an option that states \( -x < -y \) or something equivalent. Based on the analysis, we find that this corresponds to option 2.

### Final Answer:
The correct statement is option 2.