7个元素集合的子集与真子集解析穷举法举例(138)

本经验通过列举方法，介绍七个元素集合{58,59,60,61,62,63,64}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、集合{58,59,60,61,62,63,64}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={58,59,60,61,62,63,64}。

二、有1个元素的子集情况

1、集合{58,59,60,61,62,63,64}，此时个数为C(7,1)=7个，列举如下：A3={58}，A4={59}，A5={60};A6={61}，A7={62}，A8={63};A9={64}；

三、有2个元素的子集情况

1、集合{58,59,60,61,62,63,64}，此时个数为C(7,2)=21个，列举如下：A10={58,59}，A11={58,60}，A12={58,61};A13={58,62}，A14={58,63}，A15={58,64};A16={59,60}，A17={59,61}，A18={59,62};A19={59,63}，A20={59,64}，A21={60,61};A22={60,62}，A23={60,63}，A24={60,64};A25={61,62}，A26={61,63}，A27={61,64};A28={62,63}，A29={62,64}，A30={63,64};

四、有3个元素的子集情况

1、集合{58,59,60,61,62,63,64}，此时个数为C(7,3)=35个，列举如下：A31={58,59,60}，A32={58,59,61}，A33={58,59,62};A34={58,59,63}，A35={58,59,64}，A36={58,60,61};A37={58,60,62}，A38={58,60,63}，A39={58,60,64};A40={58,61,62}，A41={58,61,63}，A42={58,61,64};A43={58,62,63}，A44={58,62,64}，A45={58,63,64};A46={59,60,61}，A47={59,60,62}，A48={59,60,63};

2、A49={59,60,64}，A50={59,61,62}，A51={59,61,63};A52={59,61,64}，A53={59,62,63}，A54={59,62,64};A55={59,63,64}，A56={60,61,62}，A57={60,61,63};A58={60,61,64}，A59={60,62,63}，A60={60,62,64};A61={60,63,64}，A62={61,62,63}，A63={61,62,64};A64={61,63,64}, A65={62,63,64};

五、有4个元素的子集情况

1、集合{58,59,60,61,62,63,64}，此时个数为C(7,4)=C(7,3)=35个，列举如下：A66={58,59,60,61}，A67={58,59,60,62};A68={58,59,60,63}, A69={58,59,60,64};A70={58,59,61,62}，A71={58,59,61,63};A72={58,59,61,64}，A73={58,59,62,63};A74={58,59,62,64}, A75={58,59,63,64};A76={58,60,61,62}, A77={58,60,61,63};A78={58,60,61,64}, A79={58,60,62,63};A80={58,60,62,64}, A81={58,60,63,64};

2、A82={58,61,62,63}, A83={58,61,62,64};A84={58,61,63,64}, A85={58,62,63,64};A86={59荑樊综鲶,60,61,62}, A87={59,60,61,63};A88={59,60,61,64}, A89={59,60,62,63};A90={59,60,62,64}, A91={59,60,63,64};A92={59,61,62,63}, A93={59,61,62,64};A94={59,61,63,64}, A95={59,62,63,64};A96={60,61,62,63}, A97={60,61,62,64};A98={60,61,63,64}, A99={60,62,63,64};A100={61,62,63,64};

六、有5个元素的子集情况

1、集合{58,59,60,61,62,63,64}，此时个数为C(7,5)=C(7,2)=21个，列举如下：A101={58,59,60,61,62}, A102={58,59,60,61,63};A103={58,59,60,61,64}, A104={58,59,60,62,63};A105={58,59,60,62,64}, A106={58,59,60,63,64};A107={58,59,61,62,63}, A108={58,59,61,62,64};A109={58,59,61,62,64}, A110={58,59,62,63,64};

2、A111={58,60,61,62,63}, A112={58,60,61,62,64};A113={58,60,61,63,64}, A114={58,60,62,63,64};A115={58,61,62,63,64}, A116={59,60,61,62,63};A117={59,60,61,62,64}, A118={59,60,61,63,64};A119={59,60,62,63,64}, A120={59,61,62,63,64};A121={60,61,62,63,64};

七、有6个元素的子集情况

1、集合{58,59,60,61,62,63,64}，‍此时个数为C(7,6)=C(7,1)=7个，列举如下：A122={58,59,60,61,62,63};A123={58,59,60,61,62,64};A124={58,59,60,61,63,64};A125={58,59,60,62,63,64};A126={58,59,61,62,63,64};A127={58,60,61,62,63,64};A128={59,60,61,62,63,64}。