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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Inclusion (Boolean algebra) ： ウィキペディア英語版 Inclusion (Boolean algebra) In Boolean algebra (structure), the inclusion relation $a\backslash le\; b$ is defined as $ab\text{'}=0$ and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order. The inclusion relation * * $ab\text{'}=0$ * $a\text{'}+b=1$ * * $a+b=b$ * $ab=a$ The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the subset relation; in arithmetic Boolean algebra, divisibility; in the algebra of propositions, material implication; in the two-element algebra, the set . Some useful properties of the inclusion relation are: * $a\backslash le\; a+b$ * $ab\backslash le\; a$ The inclusion relation may be used to define Boolean intervals such that $a\backslash le\; x\backslash le\; b$ A Boolean algebra whose carrier set is restricted to the elements in an interval is itself a Boolean algebra. ==References== * Frank Markham Brown, ''Boolean Reasoning: The Logic of Boolean Equations'', 2nd edition, 2003, p. 52 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Inclusion (Boolean algebra)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.