1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Closure math problems
  1. A Math Problem (Replies: 14)

  2. Curvature math problem (Replies: 2)

  3. Financial math problem (Replies: 3)