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Negation AUB

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Construct the negation of each statement below without using the fol-
    lowing symbols: ∩, ∪, ⊆, ⊇, ⊂, ⊃, \, △, and =.

    x ∈ A U B


    2. Relevant equations



    3. The attempt at a solution
    I don't even know where to start. I'm completely lost. =\
     
  2. jcsd
  3. Sep 17, 2012 #2

    Zondrina

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    Well, my guess is you want to negate the statement : x ∈ AUB.

    This statement means that either x is in A or x is in B. How do you NEGATE this proposition?
     
  4. Sep 17, 2012 #3
    X is not in A or B? How do I symbolically write that? Because I can't use the union symbol. I initially thought that but it seemed too simple.
     
  5. Sep 17, 2012 #4

    Zondrina

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    The negation operator is written as : [itex]\neg[/itex]
     
  6. Sep 17, 2012 #5
    Ok, that makes sense. But I can't use the union symbol, and that's where I'm really confused. Could I say ~(A v B)? ~A ^ ~B by demorgans law.
     
  7. Sep 17, 2012 #6

    Zondrina

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    Well you're not being very clear about what statements you're trying to negate. Are they phrases that you haven't posted or is it actually the statement : x∈AUB. If you're trying to negate x∈AUB, then you can take for granted that the question is ASKING you to negate that statement, you're simply just not allowed to use the union symbol in doing it.
     
  8. Sep 17, 2012 #7
    It's actually the statement x ∈ AUB.
     
  9. Sep 17, 2012 #8

    Zondrina

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    Like I've already stated before then, if x ∈ AUB then either x is in A or x is in B. How would you negate this proposition, aka write the opposite of what this means.
     
  10. Sep 17, 2012 #9
    I would do ~(A v B), which simplifies to ~A ^ ~B. But as far as I know A and B are sets so I can't use those symbols.
     
  11. Sep 17, 2012 #10

    Zondrina

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    [itex]\neg[/itex]((x is in A)[itex]\vee[/itex](x is in B))

    The fact that A and B are sets makes no difference. Think about what I wrote there.
     
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