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Consensus theorem : ウィキペディア英語版
Consensus theorem

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In Boolean algebra, the consensus theorem or rule of consensus〔Frank Markham Brown, ''Boolean Reasoning: The Logic of Boolean Equations'', 2nd edition 2003, p. 44〕 is the identity:
:xy \vee \barz \vee yz = xy \vee \barz
The consensus or resolvent of the terms xy and \barz is yz. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.
The conjunctive dual of this equation is:
:(x \vee y)(\bar \vee z)(y \vee z) = (x \vee y)(\bar \vee z)
==Proof==

LHS = xy \vee \barz \vee (x \vee \bar)yz
= xy \vee \barz \vee xyz \vee \baryz
= xy \vee xyz \vee \barz \vee \baryz
= xy(1 \vee z) \vee \barz(1 \vee y)
= xy \vee \barz
= RHS

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「Consensus theorem」の詳細全文を読む



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