# 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.