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2 set theory problems

  1. Sep 2, 2012 #1
    1. The problem statement, all variables and given/known data

    show S1 U S2 = (S1' ∩ S2')'

    3. The attempt at a solution

    I'm pretty sure I have this right or I'm close

    Let x ∈ S1 U S2
    x ∈ S1 or x ∈ S2
    Since x ∈ S1 or S2, then x ∉ S1' and S2'
    If x ∉ S1' and S2', then x ∈ (S1' and S2')'
    Therefore, S1 U S2 = (S1' ∩ S2')'

    1. The problem statement, all variables and given/known data

    show S1 U S2 - (S1 ∩ S2') = S2

    3. The attempt at a solution

    I have not attempted this as I'm not sure how to start this one...any help would be appreciated.
     
    Last edited: Sep 2, 2012
  2. jcsd
  3. Sep 2, 2012 #2

    SammyS

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    You don't have the first part right.
     
  4. Sep 2, 2012 #3
    wow silly mistake thanks...any starting hints for 2? I can easily visualize it with a diagram...but I'm rusty with set notation.
     
  5. Sep 2, 2012 #4

    SammyS

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    Another problem with your solution to part 1 is that you have only shown that S1 U S2 ⊆ (S1' ∩ S2')' (that is, if you have truly corrected your proof). To show equality, you also need to show that S1 U S2 ⊇ (S1' ∩ S2')' .
     
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