Difference between revisions of "Equivalence (logical)"
From Encyclopedia of Mathematics
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| − | ''of two propositions (formulas) | + | {{TEX|done}} |
| + | ''of two propositions (formulas) $A$ and $B$'' | ||
| − | Two propositions | + | Two propositions $A$ and $B$ are (logically) equivalent if for each admissible choice of values of the parameters of $A$ and $B$ either both are true or both are false. For example, equivalence of equations, inequalities and systems of them means the coincidence of their solution sets. Equivalence of formulas of [[Propositional calculus|propositional calculus]] is the coincidence of the Boolean functions (cf. [[Boolean function|Boolean function]]) that they define. |
====References==== | ====References==== | ||
Latest revision as of 18:24, 16 April 2014
of two propositions (formulas) $A$ and $B$
Two propositions $A$ and $B$ are (logically) equivalent if for each admissible choice of values of the parameters of $A$ and $B$ either both are true or both are false. For example, equivalence of equations, inequalities and systems of them means the coincidence of their solution sets. Equivalence of formulas of propositional calculus is the coincidence of the Boolean functions (cf. Boolean function) that they define.
References
| [1] | P.S. Novikov, "Elements of mathematical logic" , Oliver & Boyd and Acad. Press (1964) (Translated from Russian) |
Comments
References
| [a1] | S.C. Kleene, "Mathematical logic" , Wiley (1967) |
How to Cite This Entry:
Equivalence (logical). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equivalence_(logical)&oldid=15947
Equivalence (logical). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equivalence_(logical)&oldid=15947
This article was adapted from an original article by S.N. Artemov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article