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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 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 .
[AK] Popper and others said that, if one uses the most widely accepted definition of "fitness" in modern biology (see subsection § Evolution), namely reproductive success itself, the expression "survival of the fittest" is a tautology. [AL] [AM] [AN]
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.
The pygmy mammoth is an example of insular dwarfism, a case of Foster's rule, its unusually small body size an adaptation to the limited resources of its island home.. A biological rule or biological law is a generalized law, principle, or rule of thumb formulated to describe patterns observed in living organisms.
Sometimes the following alternative definition is considered: a pps is given as a proof-verification algorithm P(A,x) with two inputs. If P accepts the pair (A,x) we say that x is a P-proof of A. P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if it is a tautology.
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 ]