You forgot a couple ...
|P and not Q||!(P -> Q)|
Hence, the relation holds.
Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.
I shouldn't have to say this, but any code, unless otherwise stated, is untested