A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation,
supremum must be replaced by infimum ,
maximum with minimum , and
conversely. In a lattice , this means that meet
and join must be interchanged, and in a Boolean
algebra , 1 and 0 must be switched.
Each of de Morgan's two laws can be derived from the other by duality.
See also Duality Principle
This entry contributed by Margherita
Barile
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References Donnellan, T. "Duality." §10 in Lattice Theory. Goodstein,
R. L. "Duality." §2.5 in Boolean
Algebra. Referenced
on Wolfram|Alpha Duality Law
Cite this as:
Barile, Margherita . "Duality Law." From MathWorld Eric
W. Weisstein . https://mathworld.wolfram.com/DualityLaw.html
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