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In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is ...
Strictly, this is not a tautology for the same reason as for East Timor.) South Vietnam (Nam being Vietnamese for "south", although the official name was the Republic of Vietnam. Strictly, this is not a tautology for the same reason as for East Timor.) Swahili Coast, "Swahili" is an Arabic adjective meaning "coastal [dweller]".
In literary criticism and rhetoric, a tautology is a statement that repeats an idea using near-synonymous morphemes, words or phrases, effectively "saying the same thing twice". [ 1 ] [ 2 ] Tautology and pleonasm are not consistently differentiated in literature. [ 3 ]
In propositional logic, tautology is either of two commonly used rules of replacement. [ 1 ] [ 2 ] [ 3 ] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs .
Tautology may refer to: Tautology (language) , a redundant statement in literature and rhetoric Tautology (logic) , in formal logic, a statement that is true in every possible interpretation
It is a manifestation of tautology by traditional rhetorical criteria. [4] Pleonasm may also be used for emphasis, or because the phrase has become established in a certain form. Tautology and pleonasm are not consistently differentiated in literature. [5]
Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.
where is a metalogical symbol meaning that is a syntactic consequence of and in some logical system; or as the statement of a functional tautology or theorem of propositional logic: ( ( P → Q ) ∧ ¬ Q ) → ¬ P {\displaystyle ((P\to Q)\land \neg Q)\to \neg P}