Equivalence (logical)

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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.


[1] P.S. Novikov, "Elements of mathematical logic" , Oliver & Boyd and Acad. Press (1964) (Translated from Russian)



[a1] S.C. Kleene, "Mathematical logic" , Wiley (1967)
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Equivalence (logical). Encyclopedia of Mathematics. URL:
This article was adapted from an original article by S.N. Artemov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article