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## duality

duality The property exhibited by the laws and rules of set algebra, the propositional calculus, and Boolean algebra that each law or rule has a dual law or rule, constructed by the simultaneous replacement of each occurrence of 0 by 1, 1 by 0, ∨ by ∧, and ∧ by ∨. Such a pair of laws or rules is then said to be self-dual. Thus de Morgan's laws, for example, are self-dual.

If a law or rule contains the partial ordering ← inherent in any lattice, then in obtaining duals this should be replaced by ≥ and vice versa; thus inequalities should be reversed.

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## duality

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