Law of excluded middle

Statement

In classical logic, for each proposition $p$, the proposition $p \lor \neg p$ is true.

Remarks

The formula $p \lor \neg p$ is a tautology. Some systems take the law as an axiom. Intuitionistic logic does not accept the law in general. The law is the basis of proof by cases on $p$ and $\neg p$.

Explanations

L1 human

The law says that there is no third option: a statement is true, or its negation is true. For example, each natural number $n$ is even or not even.