We use again our statement $~$S$~$, "*Socrates is a man*", and we add another statement $~$Q$~$, "*Socrates is not a man*".

Clearly, the two cannot be both true or false. The law of excluded middle says that either $~$P$~$ is true and $~$Q$~$ is false, or the opposite. We call $~$Q$~$ the **negation** of $~$P$~$, and write it:

$~$ Q \equiv \neg P$~$

If $~$P$~$ is true, then $~$\neg P$~$ is false; if $~$P$~$ is false, then $~$\neg P$~$ is true.