集合A={1,2,3,4,5,6,7}的128个子集

主要内容

通过列举法，详细列出集合A={1,2,3,4,5,6,7}的所有128个子集。

一、元素最少和最多的子集情况

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={1,2,3,4,5,6,7}。

二、有1个元素的子集情况

此时个数为C(7,1)=7个，列举如下：

A3={1}，A4={2}，A5={3};

A6={4}，A7={5}，A8={6};

A9={7}；

三、有2个元素的子集情况

此时个数为C(7,2)=21个，列举如下：

A10={1,2}，A11={1,3}，A12={1,4};

A13={1,5}，A14={1,6}，A15={1,7};

A16={2,3}，A17={2,4}，A18={2,5};

A19={2,6}，A20={2,7}，A21={3,4};

A22={3,5}，A23={3,6}，A24={3,7};

A25={4,5}，A26={4,6}，A27={4,7};

A28={5,6}，A29={5,7}，A30={6,7};

四、有3个元素的子集情况

此时个数为C(7,3)=35个，列举如下：

A31={1,2,3}，A32={1,2,4}，A33={1,2,5};

A34={1,2,6}，A35={1,2,7}，A36={1,3,4};

A37={1,3,5}，A38={1,3,6}，A39={1,3,7};

A40={1,4,5}，A41={1,4,6}，A42={1,4,7};

A43={1,5,6}，A44={1,5,7}，A45={1,6,7};

A46={2,3,4}，A47={2,3,5}，A48={2,3,6};

A49={2,3,7}，A50={2,4,5}，A51={2,4,6};

A52={2,4,7}，A53={2,5,6}，A54={2,5,7};

A55={2,6,7}，A56={3,4,5}，A57={3,4,6};

A58={3,4,7}，A59={3,5,6}，A60={3,5,7};

A61={3,6,7}，A62={4,5,6}，A63={4,5,7};

A64={4,6,7}, A65={5,6,7};

五、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={1,2,3,4}，A67={1,2,3,5};

A68={1,2,3,6}, A69={1,2,3,7};

A70={1,2,4,5}，A71={1,2,4,6};

A72={1,2,4,7}，A73={1,2,5,6};

A74={1,2,5,7}, A75={1,2,6,7};

A76={1,3,4,5}, A77={1,3,4,6};

A78={1,3,4,7}, A79={1,3,5,6};

A80={1,3,5,7}, A81={1,3,6,7};

A82={1,4,5,6}, A83={1,4,5,7};

A84={1,4,6,7}, A85={1,5,6,7};

A86={2,3,4,5}, A87={2,3,4,6};

A88={2,3,4,7}, A89={2,3,5,6};

A90={2,3,5,7}, A91={2,3,6,7};

A92={2,4,5,6}, A93={2,4,5,7};

A94={2,4,6,7}, A95={2,5,6,7};

A96={3,4,5,6}, A97={3,4,5,7};

A98={3,4,6,7}, A99={3,5,6,7};

A100={4,5,6,7};

六、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={1,2,3,4,5}, A102={1,2,3,4,6};

A103={1,2,3,4,7}, A104={1,2,3,5,6};

A105={1,2,3,5,7}, A106={1,2,3,6,7};

A107={1,2,4,5,6}, A108={1,2,4,5,7};

A109={1,2,4,5,7}, A110={1,2,5,6,7};

A111={1,3,4,5,6}, A112={1,3,4,5,7};

A113={1,3,4,6,7}, A114={1,3,5,6,7};

A115={1,4,5,6,7}, A116={2,3,4,5,6};

A117={2,3,4,5,7}, A118={2,3,4,6,7};

A119={2,3,5,6,7}, A120={2,4,5,6,7};

A121={3,4,5,6,7};

七、有6个元素的子集情况

此时个数为C(7,6)=C(7,1)=7个，列举如下：

A122={1,2,3,4,5,6};

A123={1,2,3,4,5,7};

A124={1,2,3,4,6,7};

A125={1,2,3,5,6,7};

A126={1,2,4,5,6,7};

A127={1,3,4,5,6,7};

A128={2,3,4,5,6,7}。