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Intro to set theory

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove or find counterexamples. For any sets A, B, C in a universe U:

    if A union C contained B union C then A contained B

    2. Relevant equations


    3. The attempt at a solution

    im just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks

    Let A be the empty set, and let B = C
    Then A union C = B and
    B union C = B so,
    A union C contains B union C, but A does not contain B because A is the empty set and B is not.
  2. jcsd
  3. Nov 29, 2008 #2
    Looks right to me. Just one small note: You should state that B = C is not empty at the beginning.
  4. Dec 1, 2008 #3
    alright. thank you so much!
  5. Dec 8, 2008 #4
    But what if I use the element proof for this..

    Supposed that A is a subset of B.

    Let x is an element of A u C.
    therefore, x is an element of A and x is an element of C.
    Since A is a subset of B by the definition of containment, x is an element of B.
    Since x is an element of B and x is an element of C, we have x is an element of B u C. so any element of B u C is also in A u C. therefore, A u C is a subset of B u C.

    Would this be right?
  6. Dec 8, 2008 #5


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    Science Advisor

    You are giving a counter example. You don't need a general proof, just any single counter example. You could just take A= {}, B= {1}, C= {1}.
  7. Dec 8, 2008 #6
    No, that implies x is an element of A or x is an element of C.

    Anyway, what you did here is irrelevant to your original question.
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