名校
1 . 在整数集Z中,被5除所得余数为k的所有整数组成一个“类”,记作[k],即
.给出如下四个结论:
①
;
②
;
③
;
④“整数a,b属于同一‘类’”的充要条件是“
”.
其中正确的结论的序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c66be88954b96d709d89cdecc589b29f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a05d1853d95d2978fbcf9f933c2c5.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c699ffb0b6f2c720eb81ac721b3dc2b4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8178a22db169c2ec8f5011d582d8d587.png)
④“整数a,b属于同一‘类’”的充要条件是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d827dcaa87e1525956f5a03be93655c7.png)
其中正确的结论的序号为
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2016-12-04更新
|
275次组卷
|
2卷引用:2015-2016学年湖南省株洲市二中高二上期中数学试卷
2 . 对于非空实数集
,定义
.设非空实数集
.现给出以下命题:
(1)对于任意给定符合题设条件的集合
,必有
;
(2)对于任意给定符合题设条件的集合
,必有
;
(3)对于任意给定符合题设条件的集合
,必有
;
(4)对于任意给定符合题设条件的集
,必存在常数
,使得对任意的
,恒有
.
以上命题正确的是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247e9c1c300ae341e9c02c7db92f41c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366749e18358402f70feb02785251caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabfdb27f2d2870b5bb40129f81bc255.png)
(1)对于任意给定符合题设条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2792afeb30c2254d0c1c306253158ec.png)
(2)对于任意给定符合题设条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653217ebc63b0982c9ad9b56aaa9bd55.png)
(3)对于任意给定符合题设条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a6a9a9f28d58c0b82998f6c86d500d.png)
(4)对于任意给定符合题设条件的集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf881ff2a57c5e732fd48b5cbd39540c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d533752b00dfce3f24e4647be9dfd3.png)
以上命题正确的是
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3 . 已知
为合数,且
,当
的各数位上的数字之和为质数时,称此质数为
的“衍生质数”.
(1)若
的“衍生质数”为2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
__ ;
(2)设集合
,
,则集合
中元素的个数是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97f6c1fbe60ad1b3b6451ede2c0d6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8b5b3fe713444967c19072604d2664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2f3e8b42336b396de60c5cd5d1f162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
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