7个元素集合的子集与真子集解析穷举法举例(134)

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={37,38,39,40,41,42,43}。

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={37}，A4={38}，A5={39};A6={40}，A7={41}，A8={42};A9={43}；

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={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};

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={37,38,39}，A32={37,38,40}，A泌驾台佐33={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};

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={37,3呖分甾胗8,39,40}，A67={37,38,泌驾台佐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荑樊综鲶,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};

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={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};

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={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}。