7个元素集合的子集与真子集解析穷举法举例(139)

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={61,62,63,64,65,66,67}。

1、此时个数为C(7,1)=7个，列举如下：

A3={61}，A4={62}，A5={63};

A6={64}，A7={65}，A8={66};

A9={67}；

1、此时个数为C(7,2)=21个，列举如下：

A10={61,62}，A11={61,63}，A12={61,64};

A13={61,65}，A14={61,66}，A15={61,67};

A16={62,63}，A17={62,64}，A18={62,65};

A19={62,66}，A20={62,67}，A21={63,64};

A22={63,65}，A23={63,66}，A24={63,67};

A25={64,65}，A26={64,66}，A27={64,67};

A28={65,66}，A29={65,67}，A30={66,67};

1、此时个数为C(7,3)=35个，列举如下：

A31={61,62,63}，A32={61,62,64}，A33={61,62,65};

A34={61,62,66}，A35={61,62,67}，A36={61,63,64};

A37={61,63,65}，A38={61,63,66}，A39={61,63,67};

A40={61,64,65}，A41={61,64,66}，A42={61,64,67};

A43={61,65,66}，A44={61,65,67}，A45={61,66,67};

A46={62,63,64}，A47={62,63,65}，A48={62,63,66};

2、A49={62,63,67}，A50={62,64,65}，A51={62,64,66};

A52={62,64,67}，A53={62,65,66}，A54={62,65,67};

A55={62,66,67}，A56={63,64,65}，A57={63,64,66};

A58={63,64,67}，A59={63,65,66}，A60={63,65,67};

A61={63,66,67}，A62={64,65,66}，A63={64,65,67};

A64={64,66,67}, A65={65,66,67};

1、此时个数为C(7,4)=C(7,3)=35个，列举如下：

A66={61,62,63,64}，A67={61,62,63,65};

A68={61,62,63,66}, A69={61,62,63,67};

A70={61,62,64,65}，A71={61,62,64,66};

A72={61,62,64,67}，A73={61,62,65,66};

A74={61,62,65,67}, A75={61,62,66,67};

A76={61,63,64,65}, A77={61,63,64,66};

A78={61,63,64,67}, A79={61,63,65,66};

A80={61,63,65,67}, A81={61,63,66,67};

2、A82={61,64,65,66}, A83={61,64,65,67};

A84={61,64,66,67}, A85={61,65,66,67};

A86={62,63,64,65}, A87={62,63,64,66};

A88={62,63,64,67}, A89={62,63,65,66};

A90={62,63,65,67}, A91={62,63,66,67};

A92={62,64,65,66}, A93={62,64,65,67};

A94={62,64,66,67}, A95={62,65,66,67};

A96={63,64,65,66}, A97={63,64,65,67};

A98={63,64,66,67}, A99={63,65,66,67};

A100={64,65,66,67};

1、此时个数为C(7,5)=C(7,2)=21个，列举如下：

A101={61,62,63,64,65}, A102={61,62,63,64,66};

A103={61,62,63,64,67}, A104={61,62,63,65,66};

A105={61,62,63,65,67}, A106={61,62,63,66,67};

A107={61,62,64,65,66}, A108={61,62,64,65,67};

A109={61,62,64,65,67}, A110={61,62,65,66,67};

2、 

A111={61,63,64,65,66}, A112={61,63,64,65,67};

A113={61,63,64,66,67}, A114={61,63,65,66,67};

A115={61,64,65,66,67}, A116={62,63,64,65,66};

A117={62,63,64,65,67}, A118={62,63,64,66,67};

A119={62,63,65,66,67}, A120={62,64,65,66,67};

A121={63,64,65,66,67};

1、此时个数为C(7,6)=C(7,1)=7个，列举如下：

A122={61,62,63,64,65,66};

A123={61,62,63,64,65,67};

A124={61,62,63,64,66,67};

A125={61,62,63,65,66,67};

A126={61,62,64,65,66,67};

A127={61,63,64,65,66,67};

A128={62,63,64,65,66,67}。