7个元素集合的子集与真子集解析穷举法举例(139)

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

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}。

二、有1个元素的子集情况

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}；

三、有2个元素的子集情况

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};

四、有3个元素的子集情况

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};

五、有4个元素的子集情况

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};

六、有5个元素的子集情况

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};

七、有6个元素的子集情况

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}。