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.