There was again a lot of confusion on the negation of an implication. Here is a reminder:
- The converse of "P implies Q" is defined to be "Q implies P" . It is not equivalent to "P implies Q", but it is not its negation either.
- The contrapositive of "P implies Q" is defined to be "not Q implies not P" . It is equivalent to "P implies Q", so it cannot be its negation.
- As noted above, the negation of "P implies Q" turns out to be "P and not Q".
Each of the three statements above are different.