On $R = \left \{(1,1),(1,2),(1,3),(2,2),(2,3),(3,1),(3,4),(4,5),(5,5) \right \}$
Not reflexive because (3,3) and (4,4) are missing?
Not symmetric because (2,1) ,(3,2), (4,3), (5,4) are missing?
Not transitive because (5,1) is missing??
I believe I need help with transitive relation. I understand that by definition of transitivity If I can get from one point to another in 2 steps, then I can get there in 1 step. But if there was (5,1) it would make it transitive (notice the red dashed line)?
Update:
The transitivity relation is also missing: (5,3),(5,2),(5,1),(4,2),(4,1) ?
You can't get from $5$ to $1$ in any number of steps as it is now - adding $(5,1)$ doesn't actually help transitivity. If you wanted transitivity, you'd need $(x,5)$ for all $x$, since everything has a path to $5$, along with $(y,4)$ for $y=1,2,3$, since each of those has a path to $4$, and you'd also need $(2,1)$ and $(3,2)$, since there are paths between those as well. You'd lastly need $(3,3)$, since you can get from $3$ back to $3$.