Let the relation $R = \{(0, 0); (0, 3); (1, 0); (1, 2); (2, 0); (3, 2)\}$ Find the Transitive closure of the relation.
So far this is what I'm coming up with: $\{(0, 0); (0, 3); (1, 0); (1, 2); (2, 0); (3, 2); (0, 2); (1, 3); (3, 0); (2, 3); (3, 3); (2, 2)\}$
I think this is correct so far but I'm not positive that I understand the idea of the what the transitive closure entails.
Can anyone help with this or tell me what I'm missing?
Your intuition is correct.
The relation can be drawn like this, where $n \rightarrow m$ means $(n,m) \in R$:
Now, the transitive closure is the smallest relation $R'$ s.t $R \subseteq R'$ and $R'$ is transitive.
Okay, so why is our relation not transitive now? If you can, using two arrows, go from $n$ to $m$ and from $m$ to $k$, then there must be a direct arrow from $n$ to $k$:
You should convince yourself that this new relation is not transitive either.
So you simply iterate until you end up with a transitive relation.