7个元素集合的子集与真子集解析穷举法举例(127)

7个元素集合的子集与真子集解析穷举法举例(127)

本经验通过列举方法，介绍七个元素集合的所有子集，包括真子集，使用方法为穷举法。

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={19,20,21,22,23,24,25}。

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={19}，A4={20}，A5={21};

A6={22}，A7={23}，A8={24};

A9={25}；

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={19,20}，A11={19,21}，A12={19,22};

A13={19,23}，A14={19,24}，A15={19,25};

A16={20,21}，A17={20,22}，A18={20,23};

A19={20,24}，A20={20,25}，A21={21,22};

A22={21,23}，A23={21,24}，A24={21,25};

A25={22,23}，A26={22,24}，A27={22,25};

A28={23,24}，A29={23,25}，A30={24,25};

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={19,20,21}，A32={19,20,22}，A33={19,20,23};

A34={19,20,24}，A35={19,20,25}，A36={19,21,22};

A37={19,21,23}，A38={19,21,24}，A39={19,21,25};

A40={19,22,23}，A41={19,22,24}，A42={19,22,25};

A43={19,23,24}，A44={19,23,25}，A45={19,24,25};

A46={20,21,22}，A47={20,21,23}，A48={20,21,24};

A49={20,21,25}，A50={20,22,23}，A51={20,22,24};

A52={20,22,25}，A53={20,23,24}，A54={20,23,25};

A55={20,24,25}，A56={21,22,23}，A57={21,22,24};

A58={21,22,25}，A59={21,23,24}，A60={21,23,25};

A61={21,24,25}，A62={22,23,24}，A63={22,23,25};

A64={22,24,25}, A65={23,24,25};

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={19,20,21,22}，A67={19,20,21,23};

A68={19,20,21,24}, A69={19,20,21,25};

A70={19,20,22,23}，A71={19,20,22,24};

A72={19,20,22,25}，A73={19,20,23,24};

A74={19,20,23,25}, A75={19,20,24,25};

A76={19,21,22,23}, A77={19,21,22,24};

A78={19,21,22,25}, A79={19,21,23,24};

A80={19,21,23,25}, A81={19,21,24,25};

A82={19,22,23,24}, A83={19,22,23,25};

A84={19,22,24,25}, A85={19,23,24,25};

A86={20,21,22,23}, A87={20,21,22,24};

A88={20,21,22,25}, A89={20,21,23,24};

A90={20,21,23,25}, A91={20,21,24,25};

A92={20,22,23,24}, A93={20,22,23,25};

A94={20,22,24,25}, A95={20,23,24,25};

A96={21,22,23,24}, A97={21,22,23,25};

A98={21,22,24,25}, A99={21,23,24,25};

A100={22,23,24,25};

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={19,20,21,22,23}, A102={19,20,21,22,24};

A103={19,20,21,22,25}, A104={19,20,21,23,24};

A105={19,20,21,23,25}, A106={19,20,21,24,25};

A107={19,20,22,23,24}, A108={19,20,22,23,25};

A109={19,20,22,23,25}, A110={19,20,23,24,25};

A111={19,21,22,23,24}, A112={19,21,22,23,25};

A113={19,21,22,24,25}, A114={19,21,23,24,25};

A115={19,22,23,24,25}, A116={20,21,22,23,24};

A117={20,21,22,23,25}, A118={20,21,22,24,25};

A119={20,21,23,24,25}, A120={20,22,23,24,25};

A121={21,22,23,24,25};

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={19,20,21,22,23,24};

A123={19,20,21,22,23,25};

A124={19,20,21,22,24,25};

A125={19,20,21,23,24,25};

A126={19,20,22,23,24,25};

A127={19,21,22,23,24,25};

A128={20,21,22,23,24,25}。