7个元素集合的子集与真子集解析穷举法举例(130)

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={28,29,30,31,32,33,34}。

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={28}，A4={29}，A5={30};A6={31}，A7={32}，A8={33};A9={34}；

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={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};

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={28,29,30}，A32={28,29,31}，A泌驾台佐33={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};

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={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荑樊综鲶,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};

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={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};

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={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}。