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Set theory question

  1. Nov 12, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that, for all n, for all m with 0 <= m <= n, the number of subsets of {1, . . . , n} of size m is the same as the number of subsets of {1, . . . , n} of size n − m.

    2. Relevant equations

    3. The attempt at a solution
    My problem is that I don't know where to begin. I have a vague notion that I should somehow find the powerset of all the sets of size m and n - m and compare their sizes. But I don't really know where to start.
  2. jcsd
  3. Nov 12, 2007 #2


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  4. Nov 12, 2007 #3
    C(n,m)=C(n,n-m) since order of elements in a set is not important.
  5. Nov 12, 2007 #4
    I am not familiar with combinations... what are they?

    A google search doesn't net me any useful results.
    Last edited: Nov 12, 2007
  6. Nov 13, 2007 #5

    matt grime

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    I want to choose m things. Therefore, I don't choose how many things?
  7. Nov 13, 2007 #6


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    If A is a subset of S= {1, 2,... n} with m members, how many members does S\A have? Do you see an obvious one-to-one correspondence?
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