1 . 对于非空集合
,定义其在某一运算(统称乘法)“×”下的代数结构称为“群”
,简记为
.而判断
是否为一个群,需验证以下三点:
1.(封闭性)对于规定的“×”运算,对任意
,都须满足
;
2.(结合律)对于规定的“×”运算,对任意
,都须满足
;
3.(恒等元)存在
,使得对任意
,
;
4.(逆的存在性)对任意
,都存在
,使得
.
记群
所含的元素个数为
,则群
也称作“
阶群”.若群
的“×”运算满足交换律,即对任意
,
,我们称
为一个阿贝尔群(或交换群).
(1)证明:所有实数在普通加法运算下构成群
;
(2)记
为所有模长为1的复数构成的集合,请找出一个合适的“×”运算使得
在该运算下构成一个群
,并说明理由;
(3)所有阶数小于等于四的群
是否都是阿贝尔群?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38bdb8d4c486c37ac64517ed8d60888b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1240721fdf6d8e1ed9c1158ae723637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
1.(封闭性)对于规定的“×”运算,对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9cbad1e8b405feac6e8fe403f024b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830afd1befcf1a92874b5e0bc214578d.png)
2.(结合律)对于规定的“×”运算,对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4ef2c168b3dba086f2485c3c9cc7c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d2d88c195317bf5827a1304068f26a.png)
3.(恒等元)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e6faeeed98a19d7012c921ca71a046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e4c22a6a498e197149ce29d9e98fce.png)
4.(逆的存在性)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572f76c63e3a74a90a1e6ca5ae401cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5463eaf01a62bc6a772301d9e2ad19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487cef1d4227621d9311541dec87156.png)
记群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f2eb65f2fe6546a5e318343d25fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f2eb65f2fe6546a5e318343d25fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d22c891ccf3768b616c5ddaad575aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c679fe86736064c65a292db59cb739c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
(1)证明:所有实数在普通加法运算下构成群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ba4c1c25324a8875b09d0c855a82ad.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d719c0c82f38a886db86c71bbaf8db32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d719c0c82f38a886db86c71bbaf8db32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4ef5fbf807246591e03d07ba4e3a4e.png)
(3)所有阶数小于等于四的群
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c88c74a9c2efc329f92aa4203f0f780.png)
您最近一年使用:0次
名校
2 . 设
为给定的正奇数,定义无穷数列
:
若
是数列
中的项,则记作
.
(1)若数列
的前6项各不相同,写出
的最小值及此时数列的前6项;
(2)求证:集合
是空集;
(3)记集合
正奇数
,求集合
.(若
为任意的正奇数,求所有数列
的相同元素构成的集合
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77576292d833c93bdcf4da9787ee0db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003dd0feaa12a01db4c777784889c374.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3884cadaff5a78756698d57c41f305d.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611448a63d973f73f8c0026dd38ac932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dbf7c1220f9db7d313570143f4a709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-12-21更新
|
1094次组卷
|
4卷引用:4.3 数列-求数列通项的八种方法(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)4.3 数列-求数列通项的八种方法(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)北京市西城区北师大附属实验中学2024届高三上学期12月月考数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练湖南省2024届高三数学新改革提高训练二(九省联考题型)
名校
解题方法
3 . 设
且
,n为正整数,集合
.有以下两个命题:①对任意a,存在n,使得集合S中至少有2个元素;②若存在两个n,使得S中只有1个元素,则
,那么( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88289b83c7a199bc9763152a93a2865d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67aad93107e85313c581aa0efce8cb1f.png)
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是假命题 | D.①、②都是真命题 |
您最近一年使用:0次
4 . 设数集S满足:①任意
,有
﹔②对任意x,
(x,y可以取相同值),有
或
,则称数集S具有性质P.
(1)判断数集
和
是否具有性质P,并说明理由;
(2)若数集
且
具有性质P.
(i)当
时,判断
是否一定构成等差数列,说明理由;
(ⅱ)若
,数集B中的每个元素均为自然数且
,求数集B中所有元素的和的所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8647b00cc8c8f35555c7d78cf2812c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c8b2714e2f6ddfdd6b05d3b4de1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8e5872f45d4b878b0119997cb5bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84734fbba70c0b45045fabf8090f810b.png)
(1)判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e300e8b92758e3f411495dde53d5a904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802bb7e2a3ad9686147591de5e12392b.png)
(2)若数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddc189d2c675b0e2ade4f7ed40f66fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ef80455ed7f56718cc4f1d8b837b30.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ab800bb4666f21dbe05ec239ca39ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f73eec2bbbfa166f874c39d05accb6.png)
您最近一年使用:0次
名校
解题方法
5 . 已知集合
,其中
且
,若对任意的
,都有
,则称集合
具有性质
.
(1)集合
具有性质
,求
的最小值;
(2)已知
具有性质
,求证:
;
(3)已知
具有性质
,求集合
中元素个数的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd70e76e1780a839fcbff88cd71c2fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac10f1abfec87624afd60003af4eaddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5269913f25626c9615a0851c59c20d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2aa8c7598aa438022d7ff0db9a3de7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e86a882ef57f44f0ad22836079afe1.png)
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f65336695f80a1fe2a7838a3ae17c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353433462b58fe2eba495f2589b81380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2be2cef8c6e56b2381acca7f3c0cf4.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353433462b58fe2eba495f2589b81380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2023-10-12更新
|
1774次组卷
|
5卷引用:上海市复兴高级中学2023-2024学年高二上学期期中数学试题
名校
6 . 已知数列
满足:
,对于任意实数
,集合
的元素个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359ced5cca6a8afeeaa4cad1ac7046e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9e090c72c8a1d9bbcfa7d725ad096a.png)
A.![]() | B.非零有限个 |
C.无穷多个 | D.不确定,与![]() |
您最近一年使用:0次
2023-07-04更新
|
645次组卷
|
3卷引用:上海市曹杨第二中学2022-2023学年高一下学期期末数学试题
22-23高一上·全国·期中
7 . 已知集合
,对于
的一个子集
,若存在不大于
的正整数
,使得对
中的任意一对元素
,都有
,则称
具有性质
.
(1)当
时,试判断集合
和
是否具有性质
?并说明理由;
(2)当时
,若集合
具有性质
,
①判断集合
是否一定具有性质
?并说明理由;
②求集合中
元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0742809ff6c14cf3fc76b8231dcaa786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b645549a2abd5eb88b539c01e57a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c15a2fb844bced55d1a638faab5c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9516be8b3fd9d111581ce145d50eefc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a668f4131a69c487e5c8ff6efb471fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)当时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc3aadaede28fd78943aee53f3df879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c327d0fa8d3acf720993ac6d409b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②求集合中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
8 . 已知集合
,对于集合
的非空子集
.若
中存在三个互不相同的元素
,
,
,使得
,
,
均属于
,则称集合
是集合
的“期待子集”.
(1)试判断集合
,
是否为集合
的“期待子集”;(直接写出答案,不必说明理由)
(2)如果一个集合中含有三个元素
,
,
,同时满足①
,②
,③
为偶数.那么称该集合具有性质
.对于集合
的非空子集
,证明:集合
是集合
的“期待子集”的充要条件是集合
具有性质
;
(3)若
的任意含有
个元素的子集都是集合
的“期待子集”,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a32bb35170ebe4aba4d96ad30fcfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1176ec378d071e8972ffaa3f944952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)试判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca1c611cfb42aba676bc20f876f8f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570507469628d759e4ebf323fadf79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)如果一个集合中含有三个元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d561cdf17d3a6d7d57af719cb6100c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55de080a3c1313bbd6ea5c17307c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18392c5a07408fd70ddee8a30f705305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-03-21更新
|
1040次组卷
|
6卷引用:第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)
(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)北京市丰台区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题01集合与常用逻辑(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21北京卷专题02集合(解答题)
名校
9 . 已知集合
,x、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13d30ce87fcb597b41622df51a23933.png)
,其中
.定义
,若
,则称x与y正交.
(1)若
,写出
中与x正交的所有元素;
(2)令
,若
,证明:
为偶数;
(3)若
,且A中任意两个元素均正交,分别求出
,14时,A中最多可以有多少个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511b90f652295c5c556f8630ae5985d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13d30ce87fcb597b41622df51a23933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedc27999f4df768614e022b33b414d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b02267ebc7ed6cde9d46408c7279f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5971b046d8c65732389573ad0808c42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157967918cabbed7f5d82a291cc262f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80721f50d5063cb9f835ea6fc6870285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a6fc4d929a83295d890ac7c0c09d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22111b1f07e7873e5a156d1937eaac27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d671185c2cc9c5d88029e04f4b2ccf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
您最近一年使用:0次
2023-02-03更新
|
658次组卷
|
5卷引用:上海市实验学校2022-2023学年高一上学期期末数学试题
上海市实验学校2022-2023学年高一上学期期末数学试题(已下线)难关必刷01集合的综合问题(3种题型30题专项训练)-【满分全攻略】(沪教版2020必修第一册)北京市广渠门中学2023-2024学年高二上学期10月月考数学试题(已下线)高一上学期期末复习【第一章 集合与常用逻辑用语】拔尖-举一反三系列(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
解题方法
10 . 设A是非空实数集,且
.若对于任意的
,都有
,则称集合A具有性质
;若对于任意的
,都有
,则称集合A具有性质
.
(1)写出一个恰含有两个元素且具有性质
的集合A;
(2)若非空实数集A具有性质
,求证:集合A具有性质
;
(3)设全集
,是否存在具有性质
的非空实数集A,使得集合
具有性质
?若存在,写出这样的一个集合A;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72552b86b4558a36aac78c7148d6a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4970b63e04ae03e833bdb95bd52e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出一个恰含有两个元素且具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)若非空实数集A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(3)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8afa6857b5eaf945d14a6e4d7e5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
您最近一年使用:0次
2022-11-17更新
|
622次组卷
|
7卷引用:上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题
上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)专题01集合与逻辑(15个考点)(1)(已下线)专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)北京市东城区2021-2022学年高二下学期期末统一检测数学试题北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题(已下线)专题1.8 集合与常用逻辑用语全章综合测试卷(提高篇)-举一反三系列(已下线)重难点01集合与常用逻辑用语(9种解题模型与方法)(1)