The inverse of `p implies ~| q` is :

Options

A. `~| q implies p`
B. `~| p implies q`
C. `p implies q`
D. `q implies p`

Answer

To find the inverse of the statement "P implies ~Q", we can follow these steps:

### Step 1: Understand the implication
The statement "P implies ~Q" can be written in logical notation as:
\[ P \implies \neg Q \]

### Step 2: Apply the inverse rule
The general rule for finding the inverse of an implication \( A \implies B \) is:
\[ \neg A \implies \neg B \]
Here, \( A \) is \( P \) and \( B \) is \( \neg Q \).

### Step 3: Negate both parts
Using the inverse rule, we negate both parts:
- Negate \( A \) (which is \( P \)): This gives us \( \neg P \).
- Negate \( B \) (which is \( \neg Q \)): The negation of \( \neg Q \) is \( Q \) (since negating a negation gives the original statement).

### Step 4: Write the inverse statement
Now, we can write the inverse of the original statement:
\[ \neg P \implies Q \]

### Conclusion
Thus, the inverse of the statement "P implies ~Q" is:
\[ \neg P \implies Q \]