Determine if R is an equivalence relation on set A. A = RxR. (a,b) R (c,d) iff a=c or b=d.
Reflexive- Let (a,b) be in A. (a,b) R (a,b). Therefore, a=a or b=b.
R is not an equivalence relation on set A.
Is the above correct?
This question was on my test. Initially, I said "R is an equivalence relation on set A" and it was marked wrong.
Also, in my test I wrote, Transitive- Assume (a,b)R(c,d) and (c,d)R(e,f). So, a=c or b=d and c=e or d=f. Therefore, a=c=e and b=d=f. So (a,b)R(e,f). R is transitive.
The relation is reflexive and symmetric, but not transitive.
For example, $(1,2)R(1,3)$ and $(1,3)R(0,3)$, but we do not have $(1,2) R (0,3)$.