设集合S真包含于N,S≠∅,且满足x∈S,则1+12/x-1 ∈S(1)求出只含有两个元素的集合S(2)满足题设条件的集合S共有几个?为什么?请列出
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 21:43:19
![设集合S真包含于N,S≠∅,且满足x∈S,则1+12/x-1 ∈S(1)求出只含有两个元素的集合S(2)满足题设条件的集合S共有几个?为什么?请列出](/uploads/image/z/14412338-26-8.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88S%E7%9C%9F%E5%8C%85%E5%90%AB%E4%BA%8EN%2CS%E2%89%A0%26%238709%3B%2C%E4%B8%94%E6%BB%A1%E8%B6%B3x%E2%88%88S%2C%E5%88%991%2B12%2Fx-1+%E2%88%88S%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BA%E5%8F%AA%E5%90%AB%E6%9C%89%E4%B8%A4%E4%B8%AA%E5%85%83%E7%B4%A0%E7%9A%84%E9%9B%86%E5%90%88S%EF%BC%882%EF%BC%89%E6%BB%A1%E8%B6%B3%E9%A2%98%E8%AE%BE%E6%9D%A1%E4%BB%B6%E7%9A%84%E9%9B%86%E5%90%88S%E5%85%B1%E6%9C%89%E5%87%A0%E4%B8%AA%3F%E4%B8%BA%E4%BB%80%E4%B9%88%3F%E8%AF%B7%E5%88%97%E5%87%BA)
设集合S真包含于N,S≠∅,且满足x∈S,则1+12/x-1 ∈S(1)求出只含有两个元素的集合S(2)满足题设条件的集合S共有几个?为什么?请列出
设集合S真包含于N,S≠∅,且满足x∈S,则1+12/x-1 ∈S
(1)求出只含有两个元素的集合S
(2)满足题设条件的集合S共有几个?为什么?请列出
设集合S真包含于N,S≠∅,且满足x∈S,则1+12/x-1 ∈S(1)求出只含有两个元素的集合S(2)满足题设条件的集合S共有几个?为什么?请列出
(1) 、因为S是自然数集N的真子集,且S≠∅,满足x∈S,1+12/(x-1)∈S,
当x=2时,S={2,13};当x=3时,S={3,7};当x=4时,S={4,5}.
(2)、满足题设条件的集合S共有7个.
集合S元素个数可以为2、4、6个.所有集合S如下:
{2,13};{3,7};{4,5};{2,3,7,13};{2,4,5,13};{3,4,5,7};
{2,3,4,5,7,13}.
(1)由题意得 x 只能取 2,3,4,5,7,13
则 1+12/(x-1) 为 13,7,5,4,3,2
因为x∈S,且1+12/x-1 ∈S ,所以S元素为 2,3,4,5,7,13
所以 S={2,3},S={2,4},S={2,5},S={2,7},S={2,13},
S={3,...
全部展开
(1)由题意得 x 只能取 2,3,4,5,7,13
则 1+12/(x-1) 为 13,7,5,4,3,2
因为x∈S,且1+12/x-1 ∈S ,所以S元素为 2,3,4,5,7,13
所以 S={2,3},S={2,4},S={2,5},S={2,7},S={2,13},
S={3,4},S={3,5},S={3,7},S={3,13},
S={4,5},S={4,7},S={4,13},
S={5,7},S={5,13},
S={7,13},
(2 ) n个元素的集合 公式为 2^n
因为 S共有6个元素 而且集合S真包含于N,S≠∅,
那么 S集合共有 2^6-1=63 个
S={2},S={3},S={4},S={5},S={7},S={13},
S={2,3},S={2,4},S={2,5},S={2,7},S={2,13},
S={3,4},S={3,5},S={3,7},S={3,13},
S={4,5},S={4,7},S={4,13},
S={5,7},S={5,13},
S={7,13},
S={2,3,4},S={2,3,5},S={2,3,7},S={2,3,13},
S={2,4,5},S={2,4,7},S={2,4,13},
S={2,5,7},S={2,5,13},S={2,7,13},
S={3,4,5},S={3,4,7},S={3,4,13},
S={3,5,7},S={3,5,13},S={3,7,13},
S={4,5,7},S={4,5,13},S={4,7,13},
S={5,7,13},
S={2,3,4,5},S={2,3,4,7},S={2,3,4,13},
S={2,3,5,7},S={2,3,5,13},S={2,3,7,13},
S={3,4,5,7},S={3,4,5,13},S={3,4,7,13},
S={4,5,7,13},
S={2,3,4,5,7},S={2,3,4,5,13},S={2,3,5,7,13},
S={3,4,5,7,13},
S={2,3,4,5,7,13},
收起