Statement -1: `0 lt x lt y rArr "log"_(a) x gt "log"_(a) y,"where" 0 lt a lt 1`
Statement-2: `"log"_(a) x` is a decreasing function when `0 lt a lt 1.`

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the given problem, we need to analyze the statements provided regarding logarithms with a base between 0 and 1.

### Step-by-Step Solution:

1. **Understanding the Logarithmic Function**:
The logarithmic function \( \log_a x \) is defined for \( x > 0 \). When the base \( a \) is between 0 and 1 (i.e., \( 0 < a < 1 \)), the function behaves differently than when the base is greater than 1.

**Hint**: Remember that the properties of logarithms change with the base. For bases less than 1, the function is decreasing.

2. **Analyzing Statement 1**:
The statement claims that if \( 0 < x < y \), then \( \log_a x > \log_a y \) when \( 0 < a < 1 \).

- Since \( x < y \), and because \( \log_a x \) is a decreasing function in this range, it follows that \( \log_a x \) must be greater than \( \log_a y \).

**Hint**: Use the property of decreasing functions: if \( f \) is decreasing and \( x < y \), then \( f(x) > f(y) \).

3. **Analyzing Statement 2**:
The second statement asserts that \( \log_a x \) is a decreasing function when \( 0 < a < 1 \).

- This is true because as \( x \) increases, the value of \( \log_a x \) decreases when \( a \) is between 0 and 1.

**Hint**: Graph the function \( \log_a x \) for \( 0 < a < 1 \) to visualize its decreasing nature.

4. **Conclusion**:
Both statements are true. Therefore, we can conclude that Statement 1 is correct based on the properties of logarithmic functions with bases between 0 and 1, and Statement 2 accurately describes the behavior of the logarithmic function in this context.

### Final Answer:
Both Statement 1 and Statement 2 are true.