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}。