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7个元素集合的子集与真子集解析穷举法举例(136)

2024-7-5 17:26| 发布者: haiwei| 查看: 37| 评论: 0

摘要: 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={ ...

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}。

    7个元素集合的子集与真子集解析穷举法举例(136)

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};

    7个元素集合的子集与真子集解析穷举法举例(136)

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};

     

     

    7个元素集合的子集与真子集解析穷举法举例(136)

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};

     

     

    7个元素集合的子集与真子集解析穷举法举例(136)
  • 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};

     

    7个元素集合的子集与真子集解析穷举法举例(136)

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};

     

     

     

    7个元素集合的子集与真子集解析穷举法举例(136)
  • 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};

    7个元素集合的子集与真子集解析穷举法举例(136)

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};

     

     

     

    7个元素集合的子集与真子集解析穷举法举例(136)
  • 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};

    7个元素集合的子集与真子集解析穷举法举例(136)

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}。

    7个元素集合的子集与真子集解析穷举法举例(136)

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