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Simple theorems in the algebra of sets : ウィキペディア英語版 | Simple theorems in the algebra of sets The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix ∪), intersection (infix ∩), and set complement (postfix ') of sets. These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted ′ = U; *U′ = \ ''A'' = ; *''A'' ∪ ; *U \ ''A'' = ''A''′; *''A'' \ U = ; : *''A'' ∩ ''B'' ⊆ ''A'' ⊆ ''A ''∪ ''B''. ==References==
* Edward Huntington (1904) "Sets of independent postulates for the algebra of logic," ''Transactions of the American Mathematical Society'' 5: 288-309. * Whitesitt, J. E. (1961) ''Boolean Algebra and Its Applications''. Addison-Wesley. Dover reprint, 1999.
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