Law of excluded middle

Law of excluded middle

The law of excluded middle states that for any proposition p, either p is true or its negation ¬p is true. There is no third possibility.

Statement

• p ∨ ¬p ≡ wahr (true)

Explanation

Every proposition is either true or false, never both, and never something in between. This principle is central to classical logic, but is not accepted in some non-classical logics (e.g. intuitionistic logic).

Example

• For p = "The coin shows heads", either it shows heads (p) or it does not (¬p).
• There is no middle ground.

Truth Table

p	¬p	p ∨ ¬p
T	F	T
F	T	T