Am I right in the following?

Let $$A = {1, 2, 3, 4, 5}$$ and consider the following relation on A: $$R = {(1, 2),(2, 3),(3, 4),(4, 5),(5, 1)}$$


Here I am to find the composition of R on R. I got this:




The transitive closure is


EDIT1: I added (4,1), because we have (4,5),(5,1), which would be (a,b),(b,c) and the transitive closure of those would be (4,1).


Not exactly.

a) You missed $(5,2)$, otherwise it's ok.

b) Try to prove that all pairs are in the transitive closure.


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