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.
Logic is the study of correct arguments.