1 . 已知
,
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb353115daa8100e74165461045a9ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deba64845418cb79cee8e94bd9119725.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.若![]() ![]() |
D.当![]() ![]() |
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2 . 定义全集U的子集M的特征函数
.已知
,
,则以下结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13180914d32cd9fa5b74b174d0ae611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c38edfcbc6d0348a9fc75376f629909.png)
A.若![]() ![]() ![]() |
B.对于任意![]() ![]() |
C.对于任意![]() ![]() |
D.对于任意![]() ![]() |
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2022-01-21更新
|
478次组卷
|
2卷引用:浙江省杭州市八县区2021-2022学年高二上学期期末学业水平测试数学试题
3 . 已知非空集合
,如果存在
(
且
),使得
,则称集合
具有性质
.
(1)分别判断下列集合是否具有性质
并说明理由;
①
;
②
.
(2)设m是正整数且
,集合
,求证:A具有性质
;
(3)求最小的正整数n,使得对于任意满足
且
的两个集合
和
,其中至少有一个集合具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5fd42cf3b002d9ef1627780f16c9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f490577e6b90fd4e54e588de3b404bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e869109c7cb33ecc053f63569d6f252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01a9c4d14740671afdabf9933e0a972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d871ec977913283c947608935125720a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)分别判断下列集合是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d256abcdbb1714e15a70f761126464.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3932560a63aa689fae26a5aa1b094d3.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990f78d4c9449be03045fccff2d1360a.png)
(2)设m是正整数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833c1ee6b2e531eeaad594630b3335e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5ddbfc348fd81e6be531e5c3e2f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d256abcdbb1714e15a70f761126464.png)
(3)求最小的正整数n,使得对于任意满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d3ba0288fdad44330f1dd88db72adcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5086d8f532bdec50a15171cc24a431b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833d0d3691997604885bd85d3271f212.png)
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