|Jul23-12, 05:07 AM||#1|
Urgent: Tell if this is Reflexive, transitive, symmetric?
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
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?
|Jul23-12, 11:15 AM||#2|
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