Is the following relation transitive?

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R = {(a,a),(a,c),(a,d),(b,b),(b,a),(c,c),(c,b),(c,d),(d,e),(e,a)}

I believe it is transitive however in the answer sheet I have it says it is not.

I'm following the idea that if R(a,b) and R(b,c) then if R(a,c) it is transitive.

I have tried this with respect to the above:

There is R(a,c) & R(c,d). There is also (a,d). Would this not mean that it is transitive? Thanks

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Yes, that would mean that the relation is transitive, but it would have to hold for every possible duo of pairs. For instance, note that $R(c,d)$ and $R(d,e)$, but $\not R(c,e)$. Therefore the relation is not transitive.