I am having a hard time identifying transitive relations. I think I understand those that are symmetric, but do correct me if I'm wrong.
For a set $S = \{0,1,2,3,4\}$ and a relation $Z = \{(0,2),(2,2),(2,3),(3,4)\}$ I have found:
I think it is not reflexive because there is no loop including 1.
I am struggling with this one, but I think it is transitive.
I believe this is not symmetric as there is no $(2,0), (3,2)$ or $(4,3)$.
Any help is much appreciated, I don't seem to be able to get my head around what I feel like are likely to be really simple concepts.
Best Answer
It is not reflexive because $(0,0)\notin Z$; Is is not symmetric because of the reasons you stated. For instance, $(0,2)\in Z$ but $(2,0)\notin Z$. It is not transitive; for example, $(0,2)\in Z$ and $(2,3)\in Z$ but $(0,3)\notin Z$