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Closure math problems

  1. Nov 19, 2008 #1
    1. The problem statement, all variables and given/known data
    6) Prove or give a counter-example of the following statements
    (i) (interiorA)(closure) intersect interior(A(closure)):
    (ii) interior(A(closure)) intersect (interiorA(closure)):
    (iii) interior(A union B) = interiorA union interiorB:
    (iv) interior(A intersect B) = interiorA intersect interiorB:
    (v) (A union B) (closure) = (closure) A union (closure)B:
    (vi) (A intersection B)(closure) = (closure) A intersection (closure)B:

    2. Relevant equations

    3. The attempt at a solution
    i just dont know how to do any of them
  2. jcsd
  3. Nov 20, 2008 #2


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    Re: closure

    Your first two aren't even statements. Aren't you supposed have an = sign or something? So we'll pass on those. And it's pretty weak to say "no idea on ANY of them". Try iii). Suppose A=[0,1] and B=[1,2]. Conclusion? Try to find a counterexample first. If you can't find a counterexample, then try to prove it. Some of those are not all that hard.
  4. Nov 20, 2008 #3
    Re: closure

    my mistake
    for the first one i meant to say write

    the closure (interior A) is a proper subset of the interior (closure A)

    i took A = [1,2]

    then the right side would equal [1,2] and the left would be (1,2).


    the (closure (interior A)) is not a proper subset of the (interior (closure A)), right?
  5. Nov 20, 2008 #4


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    Re: closure

    That's the idea. Just remember if it had come out to be true, that doesn't prove it's true in all cases.
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