# Negation of propositions

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.

Parents:

- Logic
Logic is the study of correct arguments.