Statement 1 : `pi^(4) gt 4^(pi)`
because
Statement 2 : The function `y=x^(x)` os decreasing `AA x gt (1)/(e ).`

Options

A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 5
B. Statement - 1 is True, Statement - 2 is True, Statement - 2 is NOT a correct explanation for Statement - 5
C. Statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True

Answer

To solve the problem, we need to analyze both statements step by step.

### Step 1: Analyze Statement 1
We need to prove that \( \pi^4 > 4^\pi \).

1. **Calculate the values of \( \pi \) and \( 4 \)**:
- The value of \( \pi \) is approximately \( 3.14 \).
- The value of \( 4 \) is \( 4 \).

2. **Calculate \( \pi^4 \)**:
\[ \pi^4 \approx (3.14)^4 \approx 97.66 \]

3. **Calculate \( 4^\pi \)**:
\[ 4^\pi = 4^{3.14} \approx 4^{3.14} \approx 64.00 \]

4. **Compare the two values**:
\[ 97.66 > 64.00 \]
Thus, \( \pi^4 > 4^\pi \) is true.

### Step 2: Analyze Statement 2
We need to analyze the function \( y = x^x \) and determine if it is decreasing for \( x > \frac{1}{e} \).

1. **Take the natural logarithm of \( y \)**:
\[ \ln(y) = x \ln(x) \]

2. **Differentiate \( \ln(y) \)**:
Using the product rule:
\[ \frac{d}{dx}(\ln(y)) = \ln(x) + 1 \]

3. **Set the derivative equal to zero to find critical points**:
\[ \ln(x) + 1 = 0 \implies \ln(x) = -1 \implies x = \frac{1}{e} \]

4. **Determine the sign of the derivative**:
- For \( x < \frac{1}{e} \), \( \ln(x) < -1 \) (negative), so \( \frac{d}{dx}(\ln(y)) < 0 \) (decreasing).
- For \( x > \frac{1}{e} \), \( \ln(x) > -1 \) (positive), so \( \frac{d}{dx}(\ln(y)) > 0 \) (increasing).

### Conclusion
- **Statement 1**: True, \( \pi^4 > 4^\pi \).
- **Statement 2**: False, the function \( y = x^x \) is increasing for \( x > \frac{1}{e} \).

### Final Answer
- Statement 1 is true and Statement 2 is false.