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Proving set theorems

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data

    I am very confused on how to prove these set theories. The statements seem to prove themselves just by the definitions of the symbols. For example:

    If A is contained or equal to B union C and A intersect B = {} (the empty set) then A is contained or equal to C.


    3. The attempt at a solution
    What I have is:

    Assume that A is contained in or equal to B union C. So, any element X that is in A will also be in either B or C. However, we also assume that A n B is the empty set, there is not element in B that is in A. Hence, any X must be contained in C. Therefore A is contained in or equal to C.

    This seems too easy... What am I assuming that i need to prove?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 2, 2009 #2

    Dick

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    Homework Helper

    It may seem too easy. But that is pretty much the whole proof. Well done. Easy theorems deserve easy proofs.
     
  4. Mar 2, 2009 #3
    THANKS, that give me confidence!
     
  5. Mar 3, 2009 #4

    HallsofIvy

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    Staff Emeritus
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    Generally, speaking, for sets, A, B, you prove "A = B" by proving "A is a subset of B" and "B is a subset of A".

    And you prove "A is a subset of B" by starting "if x is in A" and using the definitions of A and B to conclude "x is in B".
     
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