Statement-1 : ` ( p ^^ ~ q) ^^ (~ p ^^ q)` is a fallacy.
Statement -2: ` ( p to q) harr ( ~ q to ~ p)` is a tautology .

Options

A. Statement-1 is True, Statement -2 is Ture, Statement -2 is a correct explanation for statement -3
B. Statement-1 is True, Statement -2 is True,, Statement -2 is not a correct explanation for statement -3
C. Statement -1 is True , Statement -2 is false.
D. Statement -1 is False, statement -2 is True.

Explanation

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

### Step 1: Analyze Statement 1
**Statement 1:** \( (p \land \neg q) \land (\neg p \land q) \)

To determine if this statement is a fallacy (always false), we can create a truth table for the expression.

| p | q | \( \neg p \) | \( \neg q \) | \( p \land \neg q \) | \( \neg p \land q \) | \( (p \land \neg q) \land (\neg p \land q) \) |
|---|---|-------------|--------------|----------------------|----------------------|-----------------------------------------------|
| T | T | F | F | F | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | F | T | F |
| F | F | T | T | F | F | F |

From the truth table, we see that \( (p \land \neg q) \land (\neg p \land q) \) is false for all combinations of truth values for \( p \) and \( q \). Therefore, Statement 1 is indeed a fallacy.

### Step 2: Analyze Statement 2
**Statement 2:** \( (p \to q) \iff (\neg q \to \neg p) \)

We can also create a truth table for this expression.

| p | q | \( \neg p \) | \( \neg q \) | \( p \to q \) | \( \neg q \to \neg p \) | \( (p \to q) \iff (\neg q \to \neg p) \) |
|---|---|-------------|--------------|----------------|-------------------------|------------------------------------------|
| T | T | F | F | T | T | T |
| T | F | F | T | F | F | T |
| F | T | T | F | T | T | T |
| F | F | T | T | T | T | T |

From the truth table, we see that \( (p \to q) \iff (\neg q \to \neg p) \) is true for all combinations of truth values for \( p \) and \( q \). Therefore, Statement 2 is a tautology.

### Conclusion
- Statement 1 is a fallacy (always false).
- Statement 2 is a tautology (always true).

### Final Answer
- Statement 1 is true (it is a fallacy).
- Statement 2 is true (it is a tautology).