1 . 设
,子集
之积数定义为G中所有元素之乘积(空集的积数为零),求X中所有偶数个元素之子集的积数的总和是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32af3d6a5ce492722fd0f9c21f4b4843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dbe3f7060e59bb7899852205ea137be.png)
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2 . 已知非空正实数有限集合A,定义集合
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b65fc3cd4d73993db28934c2584ba44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33da439cbb5d0c47765d0009f80fa969.png)
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3 . 设集合
,且
,则
有_______ 个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26048025cda0673e1429af69766fccc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9663bdc8c7cd237b9d59f0e760ad5a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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4 . 设
为集合
的子集,若存在正整数
,使得对任意整数
,总能找到正实数
,满足
,且
在十进制表示下的所有数字(不包括开头的0)都属于集合
,则
的最小值为___ (
表示集合
的元素个数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f78ebbeebb989d39dd0206d797a19c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1563da7b0f046a469476668a3686e8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2444763873f76ca9d92b0096b0107409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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5 . 设正整数m、n,集合
,
,
,满足对任意的
,均有:
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912b27bed96203743acc37d1aef2e6c5.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d794e8f62f7f43d2598f2e4194b4e748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e10315e9199f4f8a6a0e5ef8db7c43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c9aff377f5faead95c576d8929991a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5b1e0979ae0cafa5d2813a130e4004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb79bb271e0c7bb59abfeb641775123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912b27bed96203743acc37d1aef2e6c5.png)
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