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浙江大学学报（理学版）
浙江大学学报（理学版）  2015, Vol. 42 Issue (6): 668-671    DOI: 10.3785/j.issn.1008-9497.2015.06.006
数学与计算机科学     
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
The solution set relationship between logic equation of non-zero and non-one type and its related logic equations
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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〖TX-〗=1和FG〖TX-〗=1的解集分别为S1、S2，则F=G的解集为S1-S2；若F+G=0和F〖TX-〗+G〖TX-〗=0的解集分别为S3、S4,则F=G的解集为S3∪S4；若F·G=1和F〖TX-〗·G〖TX-〗=1的解集分别为S5、S6,则F=G的解集为S5∪S6；同时亦得到：若逻辑方程组〖JB({〗F=1G=1〖JB)〗 、〖JB({〗F=0G=0〖JB)〗 的解集分别为X1、X2，则逻辑方程F=G的解集为X1∪X2，应用此结论可解非0型、非1型及相关的逻辑方程.
关键词： 解集关系;  非0 非1型;  逻辑方程组;  证明    
Abstract: 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=G into zero type or one type, along with its corresponding counter parts and their proofs. The solution sets of equation F=G is just S1－S2 if the solution sets for the equations F+G〖TX-〗=1 and FG〖TX-〗=1 are S1 and S2, respectively. If the solution sets for the equations F+G=0 and F〖TX-〗+G〖TX-〗=0 present S3 and S4, respectively, then the solution set for equation F=G is S3 ∪ S4. Assume that the solution sets for equation FG=1 and F〖TX-〗·G〖TX-〗=1 are S5 and S6 respectively, the solution set of logic equation F=G is S5 U S6. Similarly, one infers that if the solution sets of logic equations〖JB({〗F=1G=1〖JB)〗 and 〖JB({〗F=0G=0〖JB)〗 are X1 and X2 respectively, the solution set of logic equation F=G will be X1 ∪ X2. These above results can be devoted to investigate other related logic equations with nonzero and nonone types.
出版日期: 2015-07-01
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丁殿坤
王汝亮

引用本文:

丁殿坤， 王汝亮. 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[J]. 浙江大学学报（理学版）, 2015, 42(6): 668-671.

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https://www.zjujournals.com/sci/CN/Y2015/V42/I6/668

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