SOLUTION: Given a conditional statement p --> q, find the inverse of its inverse, the inverse of its converse, and the inverse of its contrapositive.

To find the converse, swap the left and right sides of ®
To find the inverse, negate left and right sides of ®
To find the contrapositive, swap and negate left and right sides of ®

To find the inverse of the inverse of p ® q

1. First find the inverse of p ® q by negating both sides, getting
   ~p ® ~q
2. Second, find the inverse of that by negating both sides, getting
   ~~p ® ~~q which simplifies to 
   p ® q.  So the inverse of the inverse is the original statement.

----------------------------------------------------------------

To find the inverse of the contrapositive of p ® q

1. First find the contrapositive of p ® q by swapping and negating
   the left and right sides, getting
   ~q ® ~p
2. Second, find the inverse of that by negating both sides, getting
   ~~q ® ~~p which simplifies to q ® p.  So the inverse of the 
   contrapositive is the converse (of the original statement).

--------------------------
Incidentally, given an original statement:

1. The inverse of the inverse is the original statement.
2. The inverse of the converse is the contrapositive.
3. The inverse of the contrapositive is the converse.
4. The converse of the inverse is the contrapositive.
5. The converse of the converse is the original statement.
6. The converse of the contrapositive is the inverse.
7. The contrapositive of the inverse is the converse.
8. The contrapositive of the converse is the inverse.
9. The contrapositive of the contrapositive is the original statement.

Edwin