17-18高一上·上海浦东新·期中
名校
1 . 设集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ae60774f5328cb04ef69734865dc5c.png)
,如果对于
的每一个含有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
个元素的子集
,
中必有
个元素的和等于
,称正整数
为集合
的一个“相关数”
(1)当
时,判断
和
是否为集合
的“相关数”,说明理由;
(2)若
为集合
的“相关数”,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ae60774f5328cb04ef69734865dc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe872911b14948468434720e5f86f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72788b79b02ee2f81eec71afe85896c.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/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41505e5e2ee8177abc71e367a0f9d53e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cab60ea646ffebbfd60a87d6b617fa2.png)
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2 . 定义区间
,
,
,
的长度均为
,多个区间并集的长度为各区间长度之和,例如
的长度
,设
,
,其中
表示不超过
的最大整数,
.若用
表示不等式
解集区间的长度,则当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c1b4fe19a6f853f1544c3742a70d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d1288c575c8cdce97930bc32c423b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c5eff93f16be6ae7174deec80302d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0154ef2c3e41e405c4bcf6e57f4b107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164f7c44511bd68f3c00eb4478222031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee99b25cf39cb541a07e81a2ae43c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d23c80f11dcb3f7537c88cbd76a1267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575ee8b07f40772a9b87075cc609b116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fdd40d1498f9fa29754f891a6ebd98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
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2019-12-10更新
|
564次组卷
|
2卷引用:上海市七宝中学2018-2019学年高一上学期第一次月考数学试题
18-19高一上·上海浦东新·期中
名校
3 . 已知集合
,
,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
是有序数对,集合
和
中的元素个数分别为
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/97b6e6193c97593e74d8488e35119d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6228afd8854fbc3c1b05fcb0bfc5ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f15cabdc3d05988fd14408ee71a57f.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/692caeb314d16479c83b584c14b556bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6ea62c5decc77abe0039fb6e4fd40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2fef18cae151fadca86595209c317c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2212c2e3f325683a2f9599a1c661ff59.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/0a2cacc52ffe015e828a4a5f2fe5ae4f.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)
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名校
4 . 将含有
个正整数的集合
分成元素个数相等且两两没有公共元素的三个集合
、
、
,其中
,若
、
、
中的元素满足条件:
,则称
为“完并集合”.
(1)若
为“完并集合”,求
的值;
(2)对于“完并集合”
,在所有符合条件的集合
中,求元素乘积最小的集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d6f818582ff6f30e8f505ca24924e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9133f6248d2a59567661a0bbe72edb68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc5bcfe736e7c92dc99719e75697d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对于“完并集合”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc391f18afee5284d0591ef104df588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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5 . 已知由自然数组成的
元集合
,非空集合
,且对任意的
,都有
.
(1)当
时,求所有满足条件的集合
;
(2)当
时,求所有满足条件的集合
的元素总和;
(3)定义一个集合的“交替和”如下:按照递减的次序重新排列该集合的元素,然后从最大数开始交替地减、加后继的数.例如集合
的交替和是
,集合
的交替和为
.当
时,求所有满足条件的集合
的“交替和”的总和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e934e8ef0a215ea403d0fb8ab06765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af958d6c104355d6daf0d205204ec760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a765dcf0813e4874c889a13b36a1677e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294250dbd576bff3da0a1456cb9a88a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)定义一个集合的“交替和”如下:按照递减的次序重新排列该集合的元素,然后从最大数开始交替地减、加后继的数.例如集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455c49a0172a3459a4e1ed3928a5b9f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c16d2edb1f3981806da56d4145f0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d71c7e08128b830fbe9ae5dbda4c2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e617042af0a6279d70b7b7424a61f011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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名校
6 . 对于集合
,
,
,
,定义
.集合
中的元素个数记为
.规定:若集合
满足
,则称集合具
有性质
.
(1)已知集合
,
,写出
,
的值;
(2)已知集合
,其中
,证明:
有性质
;
(3)已知集合
,
有性质
,且
求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5896fefe98d407d48fb709c4fb395363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f41a0eb95a51bc64caca93cb3dc2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255a362a20eb766c90447c47894be6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd01ea3d752dd68c7746c6c799b58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9821d668a92574d1bcb97aa93dc8108b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf383bb9e68dde1d91355358d45d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82715ae3437616b568f9c45d4714781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6ca4579d3b21f827a20b3e7b7ad58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078cbd53c078b091c2bba4e55c98b2c9.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c0d49c56d6bcc3aeb47ec43fca8425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c0e5a91adcedbb06079ac61fc82e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80d440b9478c09a6870403a8bd5cf38.png)
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名校
7 . 已知
是满足下列条件的集合:①
,
;②若
,则
;③若
且
,则
.
(1)判断
是否正确,说明理由;
(2)证明:“
”是“
”的充分条件;
(3)证明:若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca05074e5a317ae45d073962bdf74dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fefe237385a2dc1b005d8dc61ef56eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c443466385f21cd3f06e2e4229add79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3143beb0df5feff68bf6dd94fdfd6b5b.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79d04bf7882fd278b9ba53b791c156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f06a4a9deb51418c20e7e7376cc807.png)
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8 . 设集合
、
均为实数集
的子集,记:
;
(1)已知
,
,试用列举法表示
;
(2)设
,当
,且
时,曲线
的焦距为
,如果
,
,设
中的所有元素之和为
,对于满足
,且
的任意正整数
、
、
,不等式
恒成立,求实数
的最大值;
(3)若整数集合
,则称
为“自生集”,若任意一个正整数均为整数集合
的某个非空有限子集中所有元素的和,则称
为“
的基底集”,问:是否存在一个整数集合既是自生集又是
的基底集?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eecb2784e8889eb4b245a31f1f5fa5d.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f92003c437fb47e29838ed60e3653e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ba400854be8c167d7c20f11f2186a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eded177e1ed7b4d3b9d011033d79aa1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3cdc4da74a1d01103655fa8311540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5779e9f5131f17cd24176bb6f26795db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若整数集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b282608bf96abda302bc3ff5dd10953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
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9 . 设
且
是E的真子集,且G具有下列两条性质:
(1)对任何
恒有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7a7d65c3eb9a864b72e1e910037102.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f371a552a36c776d9aeaa8bcbec7dd0d.png)
试证:G中的奇数的个数是4的倍数,且G中的所有数字的平方和为一个定数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e53401332dcc8f7f9844dbfeb401cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a6de9ef848053f8cfc47607e513c7c.png)
(1)对任何
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2462888fa6ea4914180d92c27d0b68dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7a7d65c3eb9a864b72e1e910037102.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f371a552a36c776d9aeaa8bcbec7dd0d.png)
试证:G中的奇数的个数是4的倍数,且G中的所有数字的平方和为一个定数
您最近一年使用:0次
名校
10 . 设
是由
个有序实数构成的一个数组,记作
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f514fd4b05c3174601a5d793f1dd9f0.png)
称为数组
的“元”,
称为
的下标,如果数组
中的每个“元”都是来自数组
中不同下标的“元”,则称
为
的子数组,定义两个数组
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979d8da595088ad5fdeb7c1c1a5eb7a.png)
的关系数为
;
(1)若
,
,设
是
的含有两个“元”的子数组,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ce9afb03546fc8f61874a087a0d24e.png)
的最大值;
(2)若
,
,且
,
为
的含有三个“元”
的子数组,求
的最大值;
(3)若数组
中的“元”满足
,设数组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6c00feaa470ac6b13a6d5fee720fe5.png)
含有
四个“元”
,且
,求
与
的所有含有三个“元”
的子数组的关系数的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1b7e8ddb8c23733d2130411bb3f226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f514fd4b05c3174601a5d793f1dd9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c59e1cc0af72539dfde156a92090d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c3af219cfbba8e83e2445a8b2e6d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979d8da595088ad5fdeb7c1c1a5eb7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa84fced8d6a4e2aceebd5f283eba3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f009ed2caec247d38e1d2634d38728.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baafaf44bfc4465bf27609b5074d36d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84db1e50fa9758c98eeeeb23cf915218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ce9afb03546fc8f61874a087a0d24e.png)
的最大值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5afb01638df223c961aa642a81a34c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a320289ced1c5d9f21f64798b6d9da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f9223bc24df8d429d743692fff7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
的子数组,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ce9afb03546fc8f61874a087a0d24e.png)
(3)若数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269b6323a15f70e67290637cb94ebf9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a875cb417fccdeed5374f1a9201f97ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6c00feaa470ac6b13a6d5fee720fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d0aea7b7bcbd8bf1ef02c406f601ec.png)
四个“元”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd32d673b7d927a36f8ce7069b685b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f319f61918e56005b85ac9122be987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6c00feaa470ac6b13a6d5fee720fe5.png)
的子数组的关系数的最大值;
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