If A, then B.
Not A.
Therefore, not B.

This is an invalid argument. Wrong. Bad. It is also a commonly asserted deduction in human debate.


If I created a new writeup, I will gain experience.
I did not create a new writeup.
Therefore, I did not gain experience.

This one is obvious: There are other ways to gain experience. What if someone just cooled one of your old writeups?

This one's a bit tougher:

If I have faith in an organized religion, I can gain greater peace of mind.
I do not have faith in organized religion.
Therefore, I cannot gain greater peace of mind.

Same logic. And it is wrong for exactly the same reason -- no more, no less.

(Note: This type of argument can be valid if and only if you use a biconditional if)