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Urgent: Tell if this is Reflexive, transitive, symmetric?

  1. Jul 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine if the following relation is reflexive, transitive, symmetric or anti-symmetric.
    (A,B) element of R(relation) if for every epsilon > 0, there exists a element of A and b element of B with |a-b| < epsilon.

    2. Relevant equations



    3. The attempt at a solution
    I already proved that this is a reflexive relation (please correct me if I'm wrong):
    Let (A,B) be in R.
    Prove that (A,A) is also in R.
    NTS: For all a element of A and b element of A, |a-b| < epsilon ; epsilon>0
    Proof:
    Let a be element of A and b element of A (also).
    |a E A - b E A| ?< epsilon
    for simplicity we can write it: |a-a| < epsilon, which is true for all a and b because there's a chance that a and b will be equal since they're taken in the same set. We are sure that 0 < epsilon because epsilon > 0 by our assumption.

    Now, how can I show that this is also transitive? and symmetric or antisymmetric?
    Minor question, do I need to confirm that sets A and B are mutually exclusive to each other?
    Thanks.
     
  2. jcsd
  3. Jul 23, 2012 #2

    LCKurtz

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    You haven't told us what A and B are. One might guess they are (non-empty?) subsets of the real numbers. Is that right?

    To prove R is reflexive you need to show (A,A) in R for all A. You don't start with "Let (A,B) in R".
    That is a very confused paragraph. All you need to write is: Suppose ##\epsilon > 0##. Pick any a in A (A is non-empty?). ##|a - a|=0 < \epsilon## so (A,A) is in R.
    Write down carefully what you need to prove as a first step. If it seems reasonable, try to prove it, otherwise see if you can make a counterexample.
    Who knows? Like I said above, you haven't even told us what A and B are.
     
    Last edited: Jul 23, 2012
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