The inverse of contra-positive of p → q is

Options

A. ~p `rarr` q
B. ~p `rarr` ~ q
C. ` q rarr p`
D. `~ q rarr p `

Answer

To solve the question "The inverse of the contrapositive of p → q," we will follow these steps:

### Step 1: Identify the original statement
The original statement is \( p \to q \).

### Step 2: Find the contrapositive
The contrapositive of a statement \( p \to q \) is obtained by negating both the hypothesis and the conclusion, and then reversing them.

- The negation of \( p \) is \( \neg p \).
- The negation of \( q \) is \( \neg q \).

Thus, the contrapositive of \( p \to q \) is:
\[ \neg q \to \neg p \]

### Step 3: Find the inverse of the contrapositive
The inverse of a statement is obtained by negating both parts of the statement.

For the contrapositive \( \neg q \to \neg p \):
- The negation of \( \neg q \) is \( q \).
- The negation of \( \neg p \) is \( p \).

Thus, the inverse of the contrapositive \( \neg q \to \neg p \) is:
\[ q \to p \]

### Conclusion
The inverse of the contrapositive of \( p \to q \) is:
\[ q \to p \]