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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 Two-element Boolean algebra ： ウィキペディア英語版 Two-element Boolean algebra In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose ''underlying set'' (or universe or ''carrier'') ''B'' is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that ''B'' = . Paul Halmos's name for this algebra "2" has some following in the literature, and will be employed here. ==Definition== ''B'' is a partially ordered set and the elements of ''B'' are also its bounds. An operation of arity ''n'' is a mapping from ''B''n to ''B''. Boolean algebra consists of two binary operations and unary complementation. The binary operations have been named and notated in various ways. Here they are called 'sum' and 'product', and notated by infix '+' and '∙', respectively. Sum and product commute and associate, as in the usual algebra of real numbers. As for the order of operations, brackets are decisive if present. Otherwise '∙' precedes '+'. Hence ''A∙B + C'' is parsed as ''(A∙B) + C'' and not as ''A∙(B + C)''. Complementation is denoted by writing an overbar over its argument. The numerical analog of the complement of ''X'' is 1 − ''X''. In the language of universal algebra, a Boolean algebra is a $\backslash langle\; B,+,.,\backslash overline,1,0\backslash rangle$ algebra of type $\backslash langle\; 2,2,1,0,0\backslash rangle$. Either one-to-one correspondence between and yields classical bivalent logic in equational form, with complementation read as NOT. If 1 is read as ''True'', '+' is read as OR, and '∙' as AND, and vice versa if 1 is read as ''False''. 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「Two-element 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.