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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 Commutativity of conjunction ： ウィキペディア英語版 Commutativity of conjunction In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic. It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition. == Formal notation == ''Commutativity of conjunction'' can be expressed in sequent notation as: : $(P\; \backslash and\; Q)\; \backslash vdash\; (Q\; \backslash and\; P)$ and : $(Q\; \backslash and\; P)\; \backslash vdash\; (P\; \backslash and\; Q)$ where $\backslash vdash$ is a metalogical symbol meaning that $(Q\; \backslash and\; P)$ is a syntactic consequence of $(P\; \backslash and\; Q)$, in the one case, and $(P\; \backslash and\; Q)$ is a syntactic consequence of $(Q\; \backslash and\; P)$ in the other, in some logical system; or in rule form: :$\backslash frac$ and :$\backslash frac$ where the rule is that wherever an instance of "$(P\; \backslash and\; Q)$" appears on a line of a proof, it can be replaced with "$(Q\; \backslash and\; P)$" and wherever an instance of "$(Q\; \backslash and\; P)$" appears on a line of a proof, it can be replaced with "$(P\; \backslash and\; Q)$"; or as the statement of a truth-functional tautology or theorem of propositional logic: :$(P\; \backslash and\; Q)\; \backslash to\; (Q\; \backslash and\; P)$ and :$(Q\; \backslash and\; P)\; \backslash to\; (P\; \backslash and\; Q)$ where $P$ and $Q$ are propositions expressed in some formal system. 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「Commutativity of conjunction」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.