名校
1 . 已知集合
为非空数集,定义
.
(1)若集合
,请证明
,并直接写出集合
;
(2)若
且
,集合
,求
的最小值;
(3)若集合
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1218ca84c0ea386cc4af4a7d25fb7d.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd6edb659be68495364855860dca3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e7fd6bf379008c85f6cf6f85871a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ca33894cfd022eb3a57cfde78f06b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3489591aa8bf18d0c4c4363964c234db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
您最近一年使用:0次
名校
2 . (1)已知m是实数,集合
,
.求证:“
”是“
”的充要条件.
(2)设
.证明:若
是奇数,则n也是奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0274ba49bbad8b3179d628e3d7025cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6e153c5b9e2e807125326fd904644c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e851796d98eb47a8d17f4e1b4cea196.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
您最近一年使用:0次
2020-10-27更新
|
459次组卷
|
8卷引用:上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题
上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题上海市奉贤区致远高级中学2021-2022学年高一上学期10月评估数学试题(已下线)1.2 充分条件与必要条件(第2课时)上海市奉贤区致远高级中学2022-2023学年高一上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高一上学期9月月考数学试题(已下线)1.4 充分条件与必要条件(5大题型)精练-【题型分类归纳】(已下线)专题04充分条件与必要条件-【倍速学习法】(人教A版2019必修第一册)(已下线)专题04常用逻辑用语-【倍速学习法】(沪教版2020必修第一册)
名校
3 . 已知函数
的定义域为
.
(1)若非空集合
满足
,求实数a的取值范围;
(2)若
,用定义证明:
是定义域上的严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81a414323589af4ed230c17aa2faf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26322bd1e71fa74bb84a3ac150414a2.png)
(1)若非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f061ce46cb17bd8339322b4ed04219b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9afa6ca3c54f758947c5ece1a2e71b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69f28de04e6340b47f82e84446b83a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
您最近一年使用:0次
名校
4 . 设集合
,称坐标
在平面直角坐标系中对应的点P为A中元素a的格点.
(1)证明:若
则
.
(2)A中的元素
所对应的格点记作
(
),现将A中所有元素进行排序,使得
,在平面直角坐标系中,求以
为顶点的三角形面积.
(3)已知集合
,若
至少有2个元素,最多有5个元素,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799adb7e4c8ebf9a30182e46e56f3192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cc05fe570763e4af0ff4672e2d09e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae4202aa738ce97198687198555c84c.png)
(2)A中的元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf99487d7860d017c0747ff966edfd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019123b8c298384939e99ef5e37720d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8c195da3f1e6e13cc9fc7aca43e17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a0c3c4114915039e38b671bb707c09.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63728e5600559674a6bb03a0f183007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-10-07更新
|
197次组卷
|
2卷引用:江苏省连云港市灌南高级中学2023-2024学年高一上学期第一次月考数学试题
名校
5 . 设集合
为非空数集,定义
.
(1)若集合
,直接写出集合
及
;
(2)若集合
且
,求证
;
(3)若集合
且
,求
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e32ae0e537ab483485e3dc6628b2f3a.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce46889ee6889ca41c5bd19eaf0e242f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4d331fa6921e8ebc0b1fc4affd22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
6 . 已知集合
,
.
(1)若
,均有
,求实数
的取值范围;
(2)若
,设
,
,求证:
是
成立的必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdd554d014590a23cfac06de3bda440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac39d8afe38aca6b52b43641a274ea54.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd170c506a8ce70f550f5751ae016ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653bcf7b627c3b87fcb310732313d9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df3000f987277819847391e0548c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba27566052abbb25340b6499ae3044a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7848c89302a41e9576530313fc3e61b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40961f2dcdf88ac84a8f739317b191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2022-11-24更新
|
236次组卷
|
5卷引用:河南省学校联盟2022-2023学年高一上学期期中联考数学A试题
名校
解题方法
7 . 已知集合
,
,其中
.
(1)当
时,求集合A,B;
(2)问:
是
的什么条件?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480a320ae2f16e2dc7b2663e485f1e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b97e9b570994b69b565f2eff474ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44aca6c00903b9dd306287ba3bb91035.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)问:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c67a7e28dba059006021a2e2105f538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
您最近一年使用:0次
名校
8 . 已知集合
,集合
,集合
,且集合
满足
,
.
(1)求实数
的值.
(2)对集合
,其中
.定义由
中的元素构成两个相应的集合
,
,其中
是有序实数对,集合
和
中的元素的个数分别为
和
,若对任意的
总有
,则称集合
具有性质
.
①请检验集合
与
是否具有性质
,并对其中具有性质
的集合,写出相应的集合
和
.
②试判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1fd5e97a412914f4f8e650fcc63358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0945b9f47f37e913573a970c9c0f66e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fc06717e9b476d78e50a4ceed8564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725e7e04c2a89481457c20d6438dab0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f75ed8f6ace26756031eb3d813db6c0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de04e7bd1c120d55e09bc0ee11be3fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609e9afd827286fb76551b16aaaebf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d00adb50063efec9a89350927d52bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457e06cd98cdcba9383e28f1b6cdc488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c745503c010711188c306e1831cf712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①请检验集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709a1f33195ab62f2da488b27a219c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c67b05f5f43a2d4371a42e65dea900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
②试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-09-23更新
|
739次组卷
|
3卷引用:江苏省南京市第二十九中学2020-2021学年高一上学期10月月考数学试题
江苏省南京市第二十九中学2020-2021学年高一上学期10月月考数学试题北京市第八十中学2021-2022学年高一上学期期中考试数学试题(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)
名校
9 . 设集合
.
(1)证明:若
,则
:
(2)已知集合
,若
的子集共有
个,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e639106311b8650c63109e02c9bae25.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ac8b620b5eca9daa7276712935ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae4202aa738ce97198687198555c84c.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78e72a3713b736a92a1cc9b48504e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2021-09-05更新
|
685次组卷
|
4卷引用:吉林省四平市第一高级中学2020-2021学年高三上学期第一次月考数学(理)试题
名校
解题方法
10 . 已知定义在
上的函数
满足:①对任意正实数x,y,都有
;②当
时,
.
(1)判断函数
在
上的单调性,并证明;
(2)若
,集合
,
(
且
),且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6521ef75f0a05fe62cdfd2fbbe0430b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91bdfdbcb82294bd3c42c5c9ae0201cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfe77025195423c01af52379d9e4984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
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2021-04-14更新
|
352次组卷
|
2卷引用:湖北省鄂东南省级示范高中教育教学改革联盟学校2018-2019学年高一上学期期中联考数学试题