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Tautology
A tautology is a logical statement in which the conclusion is equivalent to the premise. More colloquially, it is formula in propositional calculus which is always true (Simpson 1992, p. 2015; D'Angelo and West 2000, p. 33; Bronshtein and Semendyayev 2004, p. 288).
If 
is a tautology, it is written 
. A sentence whose truth
table contains only 'T' is called a tautology. The following sentences
are examples of tautologies:
 |
(1)
|
 |
(2)
|
 |
(3)
|
(Mendelson 1997, p. 26), where 
denotes AND, 
denotes "is equivalent
to," 
denotes NOT, 
denotes OR, and 
denotes implies.
See also
Contingency, Contradiction, Theorem, TrueExplore with Wolfram|Alpha
References
Bronshtein, I. N.; Semendyayev, K. A.; Musiol, G.; and Muehlig, H. Handbook of Mathematics, 4th ed. New York: Springer, 2004.Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, p. 13, 1958.D'Angelo, J. P. and West, D. B. Mathematical Thinking: Problem-Solving and Proofs, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.Mendelson, E. "Tautology." §1.2 in Introduction to Mathematical Logic, 4th ed. London, England: Chapman & Hall, pp. 17-24, 1997.Simpson, J. A. and Weiner, E. S. C. (Preparers). The Compact Oxford English Dictionary, 2nd ed. Oxford, England: Clarendon Press, 1992.Referenced on Wolfram|Alpha
TautologyCite this as:
Weisstein, Eric W. "Tautology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Tautology.html