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解题方法
1 . 已知
为实数数组,定义集合
,给定正整数m,若
,则称A为
连续生成数组.
(1)判断
是否为
连续生成数组?是否为
连续生成数组?说明理由;
(2)若
为
连续生成数组,求
的值,并说明理由;
(3)数组
是否为
连续生成数组?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ae7c0278483549695d65b1faf5d856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a9856e71c2235898b9ae8dd5b511df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66383c85540d787a9554f881e2599383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb654dbe976f077495105b21b7963d0f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4527a28b17b82e1a9c4036294529ba6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3071dd7848459f70f912d758466b12b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da92a00c5e0121accc325e50f6492fe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b94c86d13f5934d26b946c119e28f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da92a00c5e0121accc325e50f6492fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ae7c0278483549695d65b1faf5d856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105a4a76bb426a85ba65255ded2147f3.png)
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2 . 设
是一个非空集合,由
的一切子集(包括
,
自身)为元素构成的集合,称为
的幂集,记为
.
(1)当
时,写出
;
(2)证明:对任意集合
,都满足
;
(3)设
是
个两位数字形成的集合,证明:
中必有两个
的子集,其元素的数值和相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1677491ba90508b0e815b566447a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7549990c248033f634d6b243b1b2dfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
(2)证明:对任意集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6fcd46d3cf19bb064958759ff2b3a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580756dffbc89ae37acef0f48d5c1140.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e044325ad7fdaef36758daa8b9fe4456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
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2022-10-21更新
|
147次组卷
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2卷引用:北京市第四十四中学2022-2023学年高一上学期10月月考数学试题
3 . 设X和Y是两个集合,
且
.证明:
(1)
.
(2)
.
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d7786f55f767e0a301b5032cdacc79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6a1190f1f5a16833808df19c437fed.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e694ec4628362b02045e09923dfdad.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39aaaaa368cbea1c1fa8687da0d43d20.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cd3c495d19893bb8e0ad2d6b0cfba5.png)
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4 . 下列三个命题中
①若A={x|x=2n,n∈Z},B={x|x=2(n﹣1),n∈Z},则A=B;
②若M﹣{x|x=2n﹣1,n∈N},B={x|x=2n+1,n∈N},则M=N;
③若C={x|x2﹣x=0},D={x|x
,n∈Z},则C=D;
④若P={x|x=2k,k∈Z},Q={x|x=4k,k∈Z},则P⊆Q.
其中真命题的是_____ .
①若A={x|x=2n,n∈Z},B={x|x=2(n﹣1),n∈Z},则A=B;
②若M﹣{x|x=2n﹣1,n∈N},B={x|x=2n+1,n∈N},则M=N;
③若C={x|x2﹣x=0},D={x|x
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6917a0777956393ce0cc558bda845d5.png)
④若P={x|x=2k,k∈Z},Q={x|x=4k,k∈Z},则P⊆Q.
其中真命题的是
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5 . 已知六个关系式①
;②
;③
;④
;⑤
;⑥
,它们中关系表达正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b55a42b599dc185bc4a6725c6524b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c943e7fce0edb7a0813b939ffcc6e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9456d08057ffbcc0811f504319565a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220987b4505fae175db3b516a2a8715b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7718a9f4f74f7961b822956a48860c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca964f173efdd080253656e13c401ed.png)
A.3 | B.4 | C.5 | D.6 |
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2022-10-12更新
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1866次组卷
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8卷引用:北京市首都师范大学附属中学2022-2023学年高一上学期10月月考数学试题
北京市首都师范大学附属中学2022-2023学年高一上学期10月月考数学试题上海市宝山区建峰附属高中2017-2018学年高一上学期期中数学试题(已下线)第02讲 集合间的基本关系-【暑假自学课】(人教A版2019必修第一册)(已下线)专题1.2 集合间的基本关系-举一反三系列((已下线)1.2集合的基本关系-高一数学同步精品课堂(北师大版2019必修第一册)(已下线)1.2 集合间的关系(精讲)-《一隅三反》(已下线)专题01 集合及集合运算求参(1)(已下线)专题01 集合及集合运算求参(1)-【寒假分层作业】(人教A版2019必修第一册)
6 . 判断下列结论的正误(正确的打“√”,错误的打“×”).
(1)在增函数与减函数的定义中,可以把“任意两个自变量”改为“存在两个自变量”._____
(2)函数
的单调递减区间是
._____
(3)所有的单调函数都有最值._______
(4)
与
表示同一个集合.______
(5)已知定义在
上的函数
的图象是连续不断的,当
时,则方程
至少有一个实数解._______
(1)在增函数与减函数的定义中,可以把“任意两个自变量”改为“存在两个自变量”.
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
(3)所有的单调函数都有最值.
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10755c124e74c5bec5eb74aaa7ba4d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea0d4c77886f665471218ad7cc36ffb7.png)
(5)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d90ba1a4ec8651f5b0f8f415b194291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
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7 . 已知集合
=
=
=
=
,则集合
的关系为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2eb12f54c6a9fe0bc6245ade7163d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175626e28b9bd08b2c82561a95a658cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2eb12f54c6a9fe0bc6245ade7163d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11482d79a1a625ae3b80a88513ce27f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
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2017-10-02更新
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8卷引用:北京市第十二中学2019-2020学年高一上学期10月月考数学试题