Write the converse, inverse and contrapositive for the statement `(~p)impliesq`.

Answer

To solve the problem of finding the converse, inverse, and contrapositive of the statement \((\neg p) \implies q\), we will follow these steps:

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

### Step 2: Write the converse
The converse of a statement of the form \(A \implies B\) is \(B \implies A\). Here, \(A\) is \(\neg p\) and \(B\) is \(q\). Therefore, the converse is:
\[ q \implies (\neg p) \]

### Step 3: Write the inverse
The inverse of a statement \(A \implies B\) is \(\neg A \implies \neg B\). Thus, for our statement:
- \(\neg A\) is \(\neg(\neg p)\) which simplifies to \(p\)
- \(\neg B\) is \(\neg q\)

So, the inverse is:
\[ p \implies (\neg q) \]

### Step 4: Write the contrapositive
The contrapositive of a statement \(A \implies B\) is \(\neg B \implies \neg A\). Therefore, for our statement:
- \(\neg B\) is \(\neg q\)
- \(\neg A\) is \(\neg(\neg p)\) which simplifies to \(p\)

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

### Summary of Results
- **Converse**: \(q \implies (\neg p)\)
- **Inverse**: \(p \implies (\neg q)\)
- **Contrapositive**: \((\neg q) \implies p\)