列举七个元素集合}的真子集

2025-11-08 06:19:39

1、集合A为7个元素,列举该集合的全部子集。

元素最少时,即1个元素也没有,此时有子集A1=∅;

元素最多时,即有7个元素,此时有子集A2=A,即:

A2={2,-5,8,-11,14,-17,20}。

列举七个元素集合}的真子集

2、含1个元素的子集,此时有7个子集,具体如下:

A3={2},A4={-5},A5={8};

A6={-11},A7={14},A8={-17};

A9={20};

列举七个元素集合}的真子集

3、有2个元素的子集情况,此时个数为C(7,2)=21个,

A10={2,-5},A11={2,8},A12={2,-11};

A13={2,14},A14={2,-17},A15={2,20};

A16={-5,8},A17={-5,-11},A18={-5,14};

A19={-5,-17},A20={-5,20},A21={8,-11};

A22={8,14},A23={8,-17},A24={8,20};

A25={-11,14},A26={-11,-17},A27={-11,20};

A28={14,-17},A29={14,20},A30={-17,20};

列举七个元素集合}的真子集

4、有3个元素的子集情况,此时个数为C(7,3)=35个:

A31={2,-5,8},A32={2,-5,-11},A33={2,-5,14};

A34={2,-5,-17},A35={2,-5,20},A36={2,8,-11};

A37={2,8,14},A38={2,8,-17},A39={2,8,20};

A40={2,-11,14},A41={2,-11,-17},A42={2,-11,20};

A43={2,14,-17},A44={2,14,20},A45={2,-17,20};

A46={-5,8,-11},A47={-5,8,14},A48={-5,8,-17};

列举七个元素集合}的真子集

5、A49={-5,8,20},A50={-5,-11,14},A51={-5,-11,-17};

A52={-5,-11,20},A53={-5,14,-17},A54={-5,14,20};

A55={-5,-17,20},A56={8,-11,14},A57={8,-11,-17};

A58={8,-11,20},A59={8,14,-17},A60={8,14,20};

A61={8,-17,20},A62={-11,14,-17},A63={-11,14,20};

A64={-11,-17,20}, A65={14,-17,20};

列举七个元素集合}的真子集

6、有4个元素的子集情况

此时个数为C(7,4)=C(7,3)=35个,列举如下:

A66={2,-5,8,-11},A67={2,-5,8,14};

A68={2,-5,8,-17}, A69={2,-5,8,20};

A70={2,-5,-11,14},A71={2,-5,-11,-17};

A72={2,-5,-11,20},A73={2,-5,14,-17};

A74={2,-5,14,20}, A75={2,-5,-17,20};

A76={2,8,-11,14}, A77={2,8,-11,-17};

A78={2,8,-11,20}, A79={2,8,14,-17};

A80={2,8,14,20}, A81={2,8,-17,20};

列举七个元素集合}的真子集

7、 

A82={2,-11,14,-17}, A83={2,-11,14,20};

A84={2,-11,-17,20}, A85={2,14,-17,20};

A86={-5,8,-11,14}, A87={-5,8,-11,-17};

A88={-5,8,-11,20}, A89={-5,8,14,-17};

A90={-5,8,14,20}, A91={-5,8,-17,20};

A92={-5,-11,14,-17}, A93={-5,-11,14,20};

A94={-5,-11,-17,20}, A95={-5,14,-17,20};

A96={8,-11,14,-17}, A97={8,-11,14,20};

A98={8,-11,-17,20}, A99={8,14,-17,20};

A100={-11,14,-17,20};

列举七个元素集合}的真子集

8、有5个元素的子集情况

此时个数为C(7,5)=C(7,2)=21个,列举如下: 

A101={2,-5,8,-11,14}, A102={2,-5,8,-11,-17};

A103={2,-5,8,-11,20}, A104={2,-5,8,14,-17};

A105={2,-5,8,14,20}, A106={2,-5,8,-17,20};

A107={2,-5,-11,14,-17}, A108={2,-5,-11,14,20};

A109={2,-5,-11,14,20}, A110={2,-5,14,-17,20};

A111={2,8,-11,14,-17}, A112={2,8,-11,14,20};

列举七个元素集合}的真子集

9、A113={2,8,-11,-17,20}, A114={2,8,14,-17,20};

A115={2,-11,14,-17,20}, A116={-5,8,-11,14,-17};

A117={-5,8,-11,14,20}, A118={-5,8,-11,-17,20};

A119={-5,8,14,-17,20}, A120={-5,-11,14,-17,20};

A121={8,-11,14,-17,20};

列举七个元素集合}的真子集

10、有6个元素的子集情况,此时个数为C(7,6)=C(7,1)=7个:

A122={2,-5,8,-11,14,-17};

A123={2,-5,8,-11,14,20};

A124={2,-5,8,-11,-17,20};

A125={2,-5,8,14,-17,20};

A126={2,-5,-11,14,-17,20};

A127={2,8,-11,14,-17,20};

A128={-5,8,-11,14,-17,20}。

列举七个元素集合}的真子集

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