The contra-positive of p→ ~ q is

Options

A. q → ~ p
B. ~q → ~P
C. ~p → ~ q
D. p → q

Answer

To find the contrapositive of the statement \( p \rightarrow \sim q \), we will follow these steps:

### Step 1: Understand the original statement
The original statement is \( p \rightarrow \sim q \), which reads as "if \( p \) then not \( q \)".

### Step 2: Negate both parts of the implication
To find the contrapositive, we first negate both \( p \) and \( \sim q \). The negation of \( p \) is \( \sim p \), and the negation of \( \sim q \) is \( q \).

So, we have:
- Negation of \( p \) is \( \sim p \)
- Negation of \( \sim q \) is \( q \)

### Step 3: Reverse the order of the implications
Now, we reverse the order of the negated statements. The contrapositive of \( p \rightarrow \sim q \) will be \( q \rightarrow \sim p \).

### Conclusion
Thus, the contrapositive of \( p \rightarrow \sim q \) is \( q \rightarrow \sim p \).

### Final Answer
The contrapositive of \( p \rightarrow \sim q \) is \( q \rightarrow \sim p \).

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