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Math Help - Set Theory................Super-Problem.

  1. #1
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    Set Theory................Super-Problem.

    S is the set of all (h, k) with h, k non-negative integers such
    that h + k < n. Each element of S is colored red or blue, so that if (h, k)
    is red and h ≤ h, k ≤ k, then (h , k ) is also red. A type 1 subset of S has
    n blue elements with different first member and a type 2 subset of S has n
    blue elements with different second member. Show that there are the same
    number of type 1 and type 2 subsets.

    ................................. Please Help!..
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  2. #2
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    Quote Originally Posted by Arka View Post
    S is the set of all (h, k) with h, k non-negative integers such
    that h + k < n. Each element of S is colored red or blue, so that if (h, k)
    is red and h ≤ h, k ≤ k, then (h , k ) is also red
    . A type 1 subset of S has n blue elements with different first member and a type 2 subset of S has n blue elements with different second member. Show that there are the same
    number of type 1 and type 2 subsets.
    Please reread and edit this posting.
    Is the part is red really what you mean to say.
    It is always true that h\le h~\&~k\le k.
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