Difference between revisions of "Tautology"
From Encyclopedia of Mathematics
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| − | A formula of the language of propositional calculus taking the [[Truth value|truth value]] "true" independently of the truth values "true" or "false" taken by its propositional variables. Examples: | + | {{TEX|done}} |
| + | A formula of the language of propositional calculus taking the [[Truth value|truth value]] "true" independently of the truth values "true" or "false" taken by its propositional variables. Examples: $A\supset A$, $A\lor\neg A$, $(A\supset B)\supset(\neg B\supset\neg A)$. | ||
In general one can check whether a given propositional formula is a tautology by simply examining the finite set of all combinations of values of its propositional variables. | In general one can check whether a given propositional formula is a tautology by simply examining the finite set of all combinations of values of its propositional variables. | ||
Revision as of 16:40, 30 July 2014
A formula of the language of propositional calculus taking the truth value "true" independently of the truth values "true" or "false" taken by its propositional variables. Examples: $A\supset A$, $A\lor\neg A$, $(A\supset B)\supset(\neg B\supset\neg A)$.
In general one can check whether a given propositional formula is a tautology by simply examining the finite set of all combinations of values of its propositional variables.
Comments
References
| [a1] | Yu.I. Manin, "A course in mathematical logic" , Springer (1977) pp. 31, 54 (Translated from Russian) |
How to Cite This Entry:
Tautology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tautology&oldid=32584
Tautology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tautology&oldid=32584
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article