The law of the excluded middle is a law in most logical systems which states that for any proposition, either that proposition or its negation must be true.
The law of the excluded middle may be formally expressed as:
P ∨ ¬P
This is not the same as the law of noncontradiction, which states that a proposition and its negation cannot both be true. The law of the excluded middle and the law of noncontradiction may be formally represented as:
(P ∨ ¬P) ∧ ¬(P & ¬P)
Alternatively, in systems which use a symbol for an exclusive disjunction (⊕ or XOR), the laws may together be formulated as:
P ⊕ ¬P
The non-classical logic system of fuzzy logic rejects the law of the excluded middle.