If P then Q. Then we can say if not Q then not P, right?
Now we will say that P is an even number and Q is a number such when it's multiplied by itself the result is a positive number.
We will use contrapositive - Then it means that if it's not Q then it's not P. Because not P is not an even number so it's odd.
But the square of an odd number is a positive number so it's Q. We now have if not Q then Q. How it's then Q and not Q at the same time?
Maybe an example itself is not valid but I want to know if there's something that I should prove before using contrapositive statements in a proof?