7个元素的集合{1,3,5,7,9,11,13}所有子集穷举
主要内容
通过列举法，详细列出集合A={1,3,5,7,9,11,13}的所有128个子集。
※.元素最少和最多的子集情况
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={1,3,5,7,9,11,13}。
※.有1个元素的子集情况
此时个数为C(7,1)=7个，列举如下：
A3={1}，A4={3}，A5={5};
A6={7}，A7={9}，A8={11};
A9={13}；
※.有2个元素的子集情况
此时个数为C(7,2)=21个，列举如下：
A10={1,3}，A11={1,5}，A12={1,7};
A13={1,9}，A14={1,11}，A15={1,13};
A16={3,5}，A17={3,7}，A18={3,9};
A19={3,11}，A20={3,13}，A21={5,7};
A22={5,9}，A23={5,11}，A24={5,13};
A25={7,9}，A26={7,11}，A27={7,13};
A28={9,11}，A29={9,13}，A30={11,13};
※.有3个元素的子集情况
此时个数为C(7,3)=35个，列举如下：
A31={1,3,5}，A32={1,3,7}，A33={1,3,9};
A34={1,3,11}，A35={1,3,13}，A36={1,5,7};
A37={1,5,9}，A38={1,5,11}，A39={1,5,13};
A40={1,7,9}，A41={1,7,11}，A42={1,7,13};
A43={1,9,11}，A44={1,9,13}，A45={1,11,13};
A46={3,5,7}，A47={3,5,9}，A48={3,5,11};
A49={3,5,13}，A50={3,7,9}，A51={3,7,11};
A52={3,7,13}，A53={3,9,11}，A54={3,9,13};
A55={3,11,13}，A56={5,7,9}，A57={5,7,11};
A58={5,7,13}，A59={5,9,11}，A60={5,9,13};
A61={5,11,13}，A62={7,9,11}，A63={7,9,13};
A64={7,11,13},A65={9,11,13};
※.有4个元素的子集情况
此时个数为C(7,4)=C(7,3)=35个，列举如下：
A66={1,3,5,7}，A67={1,3,5,9};
A68={1,3,5,11},A69={1,3,5,13};
A70={1,3,7,9}，A71={1,3,7,11};
A72={1,3,7,13}，A73={1,3,9,11};
A74={1,3,9,13},A75={1,3,11,13};
A76={1,5,7,9},A77={1,5,7,11};
A78={1,5,7,13},A79={1,5,9,11};
A80={1,5,9,13},A81={1,5,11,13};
A82={1,7,9,11},A83={1,7,9,13};
A84={1,7,11,13},A85={1,9,11,13};
A86={3,5,7,9},A87={3,5,7,11};
A88={3,5,7,13},A89={3,5,9,11};
A90={3,5,9,13},A91={3,5,11,13};
A92={3,7,9,11},A93={3,7,9,13};
A94={3,7,11,13},A95={3,9,11,13};
A96={5,7,9,11},A97={5,7,9,13};
A98={5,7,11,13},A99={5,9,11,13};
A100={7,9,11,13};
※.有5个元素的子集情况
此时个数为C(7,5)=C(7,2)=21个，列举如下：
A101={1,3,5,7,9},A102={1,3,5,7,11};
A103={1,3,5,7,13},A104={1,3,5,9,11};
A105={1,3,5,9,13},A106={1,3,5,11,13};
A107={1,3,7,9,11},A108={1,3,7,9,13};
A109={1,3,7,9,13},A110={1,3,9,11,13};
A111={1,5,7,9,11},A112={1,5,7,9,13};
A113={1,5,7,11,13},A114={1,5,9,11,13};
A115={1,7,9,11,13},A116={3,5,7,9,11};
A117={3,5,7,9,13},A118={3,5,7,11,13};
A119={3,5,9,11,13},A120={3,7,9,11,13};
A121={5,7,9,11,13};
※.有6个元素的子集情况
此时个数为C(7,6)=C(7,1)=7个，列举如下：
A122={1,3,5,7,9,11};
A123={1,3,5,7,9,13};
A124={1,3,5,7,11,13};
A125={1,3,5,9,11,13};
A126={1,3,7,9,11,13};
A127={1,5,7,9,11,13};
A128={3,5,7,9,11,13}。