非0非1型逻辑方程与相关逻辑方程的解集关系及其应用（英文）  

The solution set relationshipbetween logic equation of non-zero and non-one type and its related logic equations

作　　者：丁殿坤[1] 王汝亮[1] 

机构地区：[1]山东科技大学基础课部,山东泰安271019

出　　处：《浙江大学学报（理学版）》2015年第6期668-671,共4页Journal of Zhejiang University（Science Edition）

基　　金：Supported by research topic funded projects of Shandong Province(J06P14)

摘　　要：给出了逻辑方程解集关系定理、将逻辑方程F=G化为0型或1型逻辑方程的方法以及相应的推论,并给予证明,得到:若F+G=1和F G=1的解集分别为S1、S2,则F=G的解集为S1-S2;若F+G=0和F+G=0的解集分别为S3、S4,则F=G的解集为S3∪S4;若F·G=1和F·G=1的解集分别为S5、S6,则F=G的解集为S5∪S6;同时亦得到{F=1F=0:若逻辑方程组、的解集分别为X1、X2,则逻辑方程F=G的解集为X1∪X2,应G=1{G=0用此结论可解非0型、非1型及相关的逻辑方程.This paper proposes a theorem on the relationship between the solution set of the logic equation and a logic equation approach which transforms the logic equation F=Ginto zero type or one type,along with its corresponding counter parts and their proofs.The solution sets of equation F=Gis just S1-S2 if the solution sets for the equations F＋G=1and F G=1are S1 and S2,respectively.If the solution sets for the equations F＋G=0and F＋G=0present S3 and S4,respectively,then the solution set for equation F=Gis S3∪ S4.Assume that the solution sets for equation FG=1and F·G=1are S5 and S6respectively,the solution set of logic equation F=Gis S5 US6.{F=1F=0Similarly,one infers that if the solution sets of logic equations and X2 respectively,the soG=1{are X1 and G=0lution set of logic equation F=G will be X1∪ X2.These above results can be devoted to investigate other related logic equations with non-zero and non-one types.

关 键 词：解集关系 非0非1型 逻辑方程组 证明 

分 类 号：O141[理学—数学]