Law of Excluded Middle

Context
The law of (the) excluded middle is one of the axioms of natural deduction.

The rule
For any statement $$p$$, either $$p$$ is true or $$p$$ is false:


 * $$\vdash p \or \neg p$$

Otherwise known as tertium non datur (Latin for "third is not given", that is, a third possibility is not possible).


 * Abbreviation: $$\textrm{LEM}$$
 * Deduced from: Nothing.
 * Depends on: Nothing.

Explanation
This is one of the Aristotelian principles upon which the whole of classical logic, and the majority of mainstream mathematics rests.

This rule is denied by the intuitionist school.

Truth Table Demonstration
Let $$v: \left\{{p}\right\} \to \left\{{T, F}\right\}$$ be an interpretation for a boolean variable $$p$$.