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Simple theorems in the algebra of sets
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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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