In short, we can never conclude a sufficient condition. However, we can conclude that a sufficient condition did not happen.
If I get a bad haircut (BHC), my girlfriend will break up with me (BU).
BHC - - - - - - - - - > BU
Let's say that my girlfriend breaks up with me. What can we conclude? Nothing. We know that it's possible that I got a bad haircut, but we cannot be certain that this is the reason. There might be a wide variety of reasons. The necessary condition does not guarantee the sufficient condition.
BU - - - - - - - - -> BHC is not valid. We cannot simply flip our sufficient and necessary conditions.
No matter what happens in my relationship, we cannot conclude that I got a bad haircut.
There is one conclusion that we can make, and that is with our contrapositive.
not BU - - - - - - - - - > not BHC
If my girlfriend did not break up with me, we can say for certain that I did not get a bad haircut. But we can never say for certain that I did get a bad haircut.
