STATEMENT-1 : ` (p rArr ~q) ^^ (~q rArr q)` is a contradication
and
STATEMENT-2 : The inverse of `p rArr ~p " is " ~p rArr p`

Options

A. (a) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. (b)Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. (c)Statement-1 is True, Statement-2 is False
D. (d)Statement-1 is False, Statement-2 is True

Answer

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

### Step 1: Analyze Statement 1
The first statement is:
\[ (p \rightarrow \neg q) \land (\neg q \rightarrow q) \]
We need to determine if this statement is a contradiction. A contradiction is a statement that is always false.

1. **Construct a truth table** for the components of the statement:
- Let \( p \) and \( q \) take values True (T) and False (F).
- The implications \( p \rightarrow \neg q \) and \( \neg q \rightarrow q \) will be evaluated.

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

From the truth table, we see that the expression \( (p \rightarrow \neg q) \land (\neg q \rightarrow q) \) is false for all combinations of \( p \) and \( q \) except when \( p \) is false and \( q \) is true. Therefore, Statement 1 is not a contradiction since it can be true in some cases.

### Step 2: Analyze Statement 2
The second statement is:
\[ \text{The inverse of } (p \rightarrow \neg p) \text{ is } (\neg p \rightarrow p) \]

1. **Understanding the inverse**:
- The inverse of an implication \( A \rightarrow B \) is \( \neg A \rightarrow \neg B \).
- Here, \( A \) is \( p \) and \( B \) is \( \neg p \).
- Therefore, the inverse of \( p \rightarrow \neg p \) is \( \neg p \rightarrow p \).

2. **Evaluate the truth of the inverse**:
- The statement \( p \rightarrow \neg p \) is a contradiction because if \( p \) is true, \( \neg p \) is false, making the implication false.
- The inverse \( \neg p \rightarrow p \) is not a contradiction. It can be true when \( p \) is false.

### Conclusion
- Statement 1 is false (not a contradiction).
- Statement 2 is true (the inverse is correctly stated).

Thus, the correct answer is that Statement 1 is false and Statement 2 is true.

### Final Answer
- **Statement 1**: False
- **Statement 2**: True