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Proving Set Stuff

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data
    My teacher gave us the following proofs:

    (AUB)' = A'n B'
    x is in (AUB)'
    x is not in AUB
    x is not in A and x is not in B
    x is in A' and x is in B'

    Therefore, x is in A'n B'

    (A n B)' = A' U B'

    x is in A'UB'
    Therefore x is in A' or x is in B'
    therefore x is not in A or x is not in B
    Therefore is in (A n B)'

    (I used U for union, n for intersection.)

    I am asked to reconstruct them using the other initial assumption about X (assume it's in the other group instead)




    2. Relevant equations



    3. The attempt at a solution

    (AUB)' = A'n B'

    is in A' n B'
    x is not in A and x is not in be.
    x is in A' and x is in B'

    How can I get to the other set, which is a union/or?
     
  2. jcsd
  3. Sep 13, 2011 #2

    micromass

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    Next line: x is not in A or in B.
    Then: ...
     
  4. Sep 13, 2011 #3
    Ahh, that's pretty much the end. So x is in (AUB)' by that alone. Thanks! I'll work on the other one and come back if I need help.
     
  5. Sep 13, 2011 #4
    My work for the second:

    (A n B)' = A' U B'

    x is in (A n B)'
    x is not in (A n B)
    x is not in A or x is not in B
    x is in A' or x is in B'
    x is in A' U B'
     
  6. Sep 13, 2011 #5

    micromass

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    That's ok!! :smile:
     
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