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={46,47,48,49,50,51,52}。

END

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={46}，A4={47}，A5={48};

A6={49}，A7={50}，A8={51};

A9={52}；

END

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={46,47}，A11={46,48}，A12={46,49};

A13={46,50}，A14={46,51}，A15={46,52};

A16={47,48}，A17={47,49}，A18={47,50};

A19={47,51}，A20={47,52}，A21={48,49};

A22={48,50}，A23={48,51}，A24={48,52};

A25={49,50}，A26={49,51}，A27={49,52};

A28={50,51}，A29={50,52}，A30={51,52};

END

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={46,47,48}，A32={46,47,49}，A33={46,47,50};

A34={46,47,51}，A35={46,47,52}，A36={46,48,49};

A37={46,48,50}，A38={46,48,51}，A39={46,48,52};

A40={46,49,50}，A41={46,49,51}，A42={46,49,52};

A43={46,50,51}，A44={46,50,52}，A45={46,51,52};

A46={47,48,49}，A47={47,48,50}，A48={47,48,51};



2

A49={47,48,52}，A50={47,49,50}，A51={47,49,51};

A52={47,49,52}，A53={47,50,51}，A54={47,50,52};

A55={47,51,52}，A56={48,49,50}，A57={48,49,51};

A58={48,49,52}，A59={48,50,51}，A60={48,50,52};

A61={48,51,52}，A62={49,50,51}，A63={49,50,52};

A64={49,51,52}, A65={50,51,52};

END

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={46,47,48,49}，A67={46,47,48,50};

A68={46,47,48,51}, A69={46,47,48,52};

A70={46,47,49,50}，A71={46,47,49,51};

A72={46,47,49,52}，A73={46,47,50,51};

A74={46,47,50,52}, A75={46,47,51,52};

A76={46,48,49,50}, A77={46,48,49,51};

A78={46,48,49,52}, A79={46,48,50,51};

A80={46,48,50,52}, A81={46,48,51,52};



2

A82={46,49,50,51}, A83={46,49,50,52};

A84={46,49,51,52}, A85={46,50,51,52};

A86={47,48,49,50}, A87={47,48,49,51};

A88={47,48,49,52}, A89={47,48,50,51};

A90={47,48,50,52}, A91={47,48,51,52};

A92={47,49,50,51}, A93={47,49,50,52};

A94={47,49,51,52}, A95={47,50,51,52};

A96={48,49,50,51}, A97={48,49,50,52};

A98={48,49,51,52}, A99={48,50,51,52};

A100={49,50,51,52};

END

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={46,47,48,49,50}, A102={46,47,48,49,51};

A103={46,47,48,49,52}, A104={46,47,48,50,51};

A105={46,47,48,50,52}, A106={46,47,48,51,52};

A107={46,47,49,50,51}, A108={46,47,49,50,52};

A109={46,47,49,50,52}, A110={46,47,50,51,52};



2

A111={46,48,49,50,51}, A112={46,48,49,50,52};

A113={46,48,49,51,52}, A114={46,48,50,51,52};

A115={46,49,50,51,52}, A116={47,48,49,50,51};

A117={47,48,49,50,52}, A118={47,48,49,51,52};

A119={47,48,50,51,52}, A120={47,49,50,51,52};

A121={48,49,50,51,52};

END

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={46,47,48,49,50,51};

A123={46,47,48,49,50,52};

A124={46,47,48,49,51,52};

A125={46,47,48,50,51,52};

A126={46,47,49,50,51,52};

A127={46,48,49,50,51,52};

A128={47,48,49,50,51,52}。

END