Statement -1 `(1/2)^7lt(1/3)^4`
`implies 7log(1/2)lt4log(1/3)implies7lt4`
Statement-2 If `axltay`, where `alt0`,x,`ygt0`, then `xgty`.
(a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1
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.

Answer

To solve the problem, we need to analyze the two statements provided and determine their truth values.

### Step 1: Analyze Statement 1
The first statement is:
\[ \left(\frac{1}{2}\right)^7 < \left(\frac{1}{3}\right)^4 \]

To check if this statement is true, we can calculate both sides:

- Calculate \(\left(\frac{1}{2}\right)^7\):
\[ \left(\frac{1}{2}\right)^7 = \frac{1}{128} \]

- Calculate \(\left(\frac{1}{3}\right)^4\):
\[ \left(\frac{1}{3}\right)^4 = \frac{1}{81} \]

Now, we compare \(\frac{1}{128}\) and \(\frac{1}{81}\):
Since \(128 > 81\), we have:
\[ \frac{1}{128} < \frac{1}{81} \]
Thus, Statement 1 is **true**.

### Step 2: Logarithmic Implication
The statement also claims:
\[ 7 \log\left(\frac{1}{2}\right) < 4 \log\left(\frac{1}{3}\right) \]

Using the property of logarithms that states \(\log(a^b) = b \log(a)\), we can rewrite the logarithms:
- \(\log\left(\frac{1}{2}\right) = \log(1) - \log(2) = -\log(2)\)
- \(\log\left(\frac{1}{3}\right) = \log(1) - \log(3) = -\log(3)\)

Thus, we have:
\[ 7(-\log(2)) < 4(-\log(3)) \]
This simplifies to:
\[ -7\log(2) < -4\log(3) \]
Multiplying both sides by -1 (which reverses the inequality):
\[ 7\log(2) > 4\log(3) \]

This does not imply \(7 < 4\). Therefore, the implication in Statement 1 is **false**.

### Step 3: Analyze Statement 2
The second statement is:
"If \(ax < ay\) where \(a < 0\), \(x, y > 0\), then \(x > y\)."

To analyze this, we can rearrange the inequality:
\[ ax < ay \implies a(x - y) < 0 \]
Since \(a < 0\), for the product \(a(x - y)\) to be less than 0, \(x - y\) must be greater than 0. Thus:
\[ x - y > 0 \implies x > y \]
This confirms that Statement 2 is **true**.

### Conclusion
- Statement 1 is **false**.
- Statement 2 is **true**.

Thus, the correct answer is:
**(d) Statement 1 is false, Statement 2 is true.**