Contradictory
Contradictory is an adjective used to describe statements, ideas, or propositions that oppose each other in such a way that they cannot both be true in the same sense at the same time. In ordinary language, a contradictory claim directly conflicts with another claim or with itself.
In logic, a proposition and its negation form a contradictory pair. The law of non-contradiction holds that
In traditional syllogistic, the term is used to describe pairs of propositions that cannot both be true:
Contradictory as a concept is related to inconsistency, paradox, and dispute. Some non-classical logics, such as