1 . 若集合
的非空子集
满足:对任意给定的
,若
,有
,则称子集
是
的“好子集”.记
为
的好子集的个数.例如:
的7个非空子集中只有
不是好子集,即
.记
表示集合
的元素个数.
(1)求
的值;
(2)若
是
的好子集,且
.证明:
中元素可以排成一个等差数列;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5c44de003475d3466981293cf5e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c469f6345826410959ea09d7e3192e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0586ec8d1d9796fb80a1250e2c0a4b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c562f247c1d691158f4038a030574c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68eafd45c1ec4b414d3553dabd8c2848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37765d2927d24d4b582423c843aebcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada01c2a8b4d92df94834a6a3929673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df6a6d73a058d13632a726c2308d66.png)
您最近一年使用:0次
解题方法
2 . 已知集合
,
,
,若
,
,
或
,则称集合A具有“包容”性.
(1)判断集合
和集合
是否具有“包容”性;
(2)若集合
具有“包容”性,求
的值;
(3)若集合C具有“包容”性,且集合C的子集有64个,
,试确定集合C.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe38d1b1e18720a878bd7442c8f094de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46de01c5104b9112a688df37eadb000.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac46c6c52fc8b8e8f76084352e1893f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3ed03b0f8fb8b88d7edf6165345c6f.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acf45d9d64697db902fe8faa15394d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
(3)若集合C具有“包容”性,且集合C的子集有64个,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65f44d4f1341a7d80897a54a6778fae.png)
您最近一年使用:0次
名校
3 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c9e547b17582b99e548037172eeff3.png)
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若n为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c9e547b17582b99e548037172eeff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677fd74842cbce34aed7073cebbd9c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若n为偶数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
您最近一年使用:0次
2024-03-12更新
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439次组卷
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2卷引用:江西省贵溪市实验中学2024届高三下学期5月高考冲刺压轴卷(一)数学试卷