7个元素集合的子集与真子集解析穷举法举例(130)

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={28,29,30,31,32,33,34}。

1、此时个数为C(7,1)=7个，列举如下：

A3={28}，A4={29}，A5={30};

A6={31}，A7={32}，A8={33};

A9={34}；

1、 

此时个数为C(7,2)=21个，列举如下：

A10={28,29}，A11={28,30}，A12={28,31};

A13={28,32}，A14={28,33}，A15={28,34};

A16={29,30}，A17={29,31}，A18={29,32};

A19={29,33}，A20={29,34}，A21={30,31};

A22={30,32}，A23={30,33}，A24={30,34};

A25={31,32}，A26={31,33}，A27={31,34};

A28={32,33}，A29={32,34}，A30={33,34};

2、 

1、此时个数为C(7,3)=35个，列举如下：

A31={28,29,30}，A32={28,29,31}，A33={28,29,32};

A34={28,29,33}，A35={28,29,34}，A36={28,30,31};

A37={28,30,32}，A38={28,30,33}，A39={28,30,34};

A40={28,31,32}，A41={28,31,33}，A42={28,31,34};

A43={28,32,33}，A44={28,32,34}，A45={28,33,34};

A46={29,30,31}，A47={29,30,32}，A48={29,30,33};

2、A49={29,30,34}，A50={29,31,32}，A51={29,31,33};

A52={29,31,34}，A53={29,32,33}，A54={29,32,34};

A55={29,33,34}，A56={30,31,32}，A57={30,31,33};

A58={30,31,34}，A59={30,32,33}，A60={30,32,34};

A61={30,33,34}，A62={31,32,33}，A63={31,32,34};

A64={31,33,34}, A65={32,33,34};

1、 

此时个数为C(7,4)=C(7,3)=35个，列举如下：

A66={28,29,30,31}，A67={28,29,30,32};

A68={28,29,30,33}, A69={28,29,30,34};

A70={28,29,31,32}，A71={28,29,31,33};

A72={28,29,31,34}，A73={28,29,32,33};

A74={28,29,32,34}, A75={28,29,33,34};

A76={28,30,31,32}, A77={28,30,31,33};

A78={28,30,31,34}, A79={28,30,32,33};

A80={28,30,32,34}, A81={28,30,33,34};

2、A82={28,31,32,33}, A83={28,31,32,34};

A84={28,31,33,34}, A85={28,32,33,34};

A86={29,30,31,32}, A87={29,30,31,33};

A88={29,30,31,34}, A89={29,30,32,33};

A90={29,30,32,34}, A91={29,30,33,34};

A92={29,31,32,33}, A93={29,31,32,34};

A94={29,31,33,34}, A95={29,32,33,34};

A96={30,31,32,33}, A97={30,31,32,34};

A98={30,31,33,34}, A99={30,32,33,34};

A100={31,32,33,34};

1、此时个数为C(7,5)=C(7,2)=21个，列举如下：

A101={28,29,30,31,32}, A102={28,29,30,31,33};

A103={28,29,30,31,34}, A104={28,29,30,32,33};

A105={28,29,30,32,34}, A106={28,29,30,33,34};

A107={28,29,31,32,33}, A108={28,29,31,32,34};

A109={28,29,31,32,34}, A110={28,29,32,33,34};

2、A111={28,30,31,32,33}, A112={28,30,31,32,34};

A113={28,30,31,33,34}, A114={28,30,32,33,34};

A115={28,31,32,33,34}, A116={29,30,31,32,33};

A117={29,30,31,32,34}, A118={29,30,31,33,34};

A119={29,30,32,33,34}, A120={29,31,32,33,34};

A121={30,31,32,33,34};

1、 

此时个数为C(7,6)=C(7,1)=7个，列举如下：

A122={28,29,30,31,32,33};

A123={28,29,30,31,32,34};

A124={28,29,30,31,33,34};

A125={28,29,30,32,33,34};

A126={28,29,31,32,33,34};

A127={28,30,31,32,33,34};

A128={29,30,31,32,33,34}。