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Abstract math, sets and logic proof

  1. Apr 2, 2012 #1
    1. The problem statement, all variables and given/known data
    If A is a set that contains a finite number of elements, we say A is a finite set. If
    A is a finite set, we write |A| to denote the number of elements in the set A. We
    also write |B| < ∞ to indicate that B is a finite set. Denote the sets X and Y by
    X = {T : T is a proper subset of P(Z) or |T| < ∞}; Y = {T element of X : T≠ ∅}
    Prove or disprove the following:
    (there exist X element of R)(∅ element of R and ( for all S element of Y)(|R|≤ |S|}


    2. Relevant equations


    3. The attempt at a solution
    I think that statement is true because of or in the statement, but I have no idea how to prove it
     
    Last edited: Apr 2, 2012
  2. jcsd
  3. Apr 2, 2012 #2
    I can't understand what it is that you are trying to show. Can you write it out in words?
     
  4. Apr 3, 2012 #3
    It s number 5 from the attachment.
     

    Attached Files:

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