已知A∪B={0,1,2,3,4,5},A∩B={1,2,3,4,5},求集合A,B,并用Venn图表示.

问题描述:

已知A∪B={0,1,2,3,4,5},A∩B={1,2,3,4,5},求集合A,B,并用Venn图表示.

∵A∩B={1,2,3,4,5},∴{1,2,3,4,5}∈A,或{1,2,3,4,5}∈B,又∵A∪B={0,1,2,3,4,5},∴0∈A,或0∈B,故A={1,2,3,4,5},B={0,1,2,3,4,5},或A={0,1,2,3,4,5},B={1,2,3,4,5},...
答案解析:由已知A∪B={0,1,2,3,4,5},A∩B={1,2,3,4,5},可得A={1,2,3,4,5},B={0,1,2,3,4,5},或A={0,1,2,3,4,5},B={1,2,3,4,5},进而可得满足条件的Venn图.
考试点:Venn图表达集合的关系及运算.
知识点:本题考查的知识点是Venn图表达集合的关系及运算,其中由已知分析出A={1,2,3,4,5},B={0,1,2,3,4,5},或A={0,1,2,3,4,5},B={1,2,3,4,5},是解答的关键.