7个元素集合的子集与真子集解析穷举法举例(134)

1、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={37,38,39,40,41,42,43}。

1、此时个数为C(7,1)=7个，列举如下：

A3={37}，A4={38}，A5={39};

A6={40}，A7={41}，A8={42};

A9={43}；

1、此时个数为C(7,2)=21个，列举如下：

A10={37,38}，A11={37,39}，A12={37,40};

A13={37,41}，A14={37,42}，A15={37,43};

A16={38,39}，A17={38,40}，A18={38,41};

A19={38,42}，A20={38,43}，A21={39,40};

A22={39,41}，A23={39,42}，A24={39,43};

A25={40,41}，A26={40,42}，A27={40,43};

A28={41,42}，A29={41,43}，A30={42,43};

1、此时个数为C(7,3)=35个，列举如下：

A31={37,38,39}，A32={37,38,40}，A33={37,38,41};

A34={37,38,42}，A35={37,38,43}，A36={37,39,40};

A37={37,39,41}，A38={37,39,42}，A39={37,39,43};

A40={37,40,41}，A41={37,40,42}，A42={37,40,43};

A43={37,41,42}，A44={37,41,43}，A45={37,42,43};

A46={38,39,40}，A47={38,39,41}，A48={38,39,42};

2、A49={38,39,43}，A50={38,40,41}，A51={38,40,42};

A52={38,40,43}，A53={38,41,42}，A54={38,41,43};

A55={38,42,43}，A56={39,40,41}，A57={39,40,42};

A58={39,40,43}，A59={39,41,42}，A60={39,41,43};

A61={39,42,43}，A62={40,41,42}，A63={40,41,43};

A64={40,42,43}, A65={41,42,43};

1、此时个数为C(7,4)=C(7,3)=35个，列举如下：

A66={37,38,39,40}，A67={37,38,39,41};

A68={37,38,39,42}, A69={37,38,39,43};

A70={37,38,40,41}，A71={37,38,40,42};

A72={37,38,40,43}，A73={37,38,41,42};

A74={37,38,41,43}, A75={37,38,42,43};

A76={37,39,40,41}, A77={37,39,40,42};

A78={37,39,40,43}, A79={37,39,41,42};

A80={37,39,41,43}, A81={37,39,42,43};

2、A82={37,40,41,42}, A83={37,40,41,43};

A84={37,40,42,43}, A85={37,41,42,43};

A86={38,39,40,41}, A87={38,39,40,42};

A88={38,39,40,43}, A89={38,39,41,42};

A90={38,39,41,43}, A91={38,39,42,43};

A92={38,40,41,42}, A93={38,40,41,43};

A94={38,40,42,43}, A95={38,41,42,43};

A96={39,40,41,42}, A97={39,40,41,43};

A98={39,40,42,43}, A99={39,41,42,43};

A100={40,41,42,43};

1、此时个数为C(7,5)=C(7,2)=21个，列举如下：

A101={37,38,39,40,41}, A102={37,38,39,40,42};

A103={37,38,39,40,43}, A104={37,38,39,41,42};

A105={37,38,39,41,43}, A106={37,38,39,42,43};

A107={37,38,40,41,42}, A108={37,38,40,41,43};

A109={37,38,40,41,43}, A110={37,38,41,42,43};

2、 

A111={37,39,40,41,42}, A112={37,39,40,41,43};

A113={37,39,40,42,43}, A114={37,39,41,42,43};

A115={37,40,41,42,43}, A116={38,39,40,41,42};

A117={38,39,40,41,43}, A118={38,39,40,42,43};

A119={38,39,41,42,43}, A120={38,40,41,42,43};

A121={39,40,41,42,43};

1、此时个数为C(7,6)=C(7,1)=7个，列举如下：

A122={37,38,39,40,41,42};

A123={37,38,39,40,41,43};

A124={37,38,39,40,42,43};

A125={37,38,39,41,42,43};

A126={37,38,40,41,42,43};

A127={37,39,40,41,42,43};

A128={38,39,40,41,42,43}。